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1. # Summer Research in Mathematics2021 Summer Research in Mathematics

Due to the COVID-19 pandemic, the 2020 Summer Research in Mathematics program was postponed to 2021 and held remotely.

MSRI's Summer Research in Mathematics program provides space, funding, and the opportunity for in-person collaboration to small groups of mathematicians, especially women and gender-expansive individuals, whose ongoing research may have been disproportionately affected by various obstacles including family obligations, professional isolation, or access to funding. Through this effort, MSRI aims to mitigate the obstacles faced by these small groups, improve the odds of research project completion, and deepen their research experience.

The ultimate goal of this program is to enhance the mathematical sciences as a whole by positively affecting the research and careers of all of its participants and assisting their efforts to maintain involvement in the research community.

Updated on Sep 15, 2021 09:25 AM PDT
2. # ProgramOffsite Simons Postdoctoral Fellowship 2021/22

Updated on Aug 03, 2021 12:35 PM PDT
3. # ProgramUniversality and Integrability in Random Matrix Theory and Interacting Particle Systems

Organizers: LEAD Ivan Corwin (Columbia University), Percy Deift (New York University, Courant Institute), Ioana Dumitriu (University of California, San Diego), Alice Guionnet (École Normale Supérieure de Lyon), Alexander Its (Indiana University--Purdue University), Herbert Spohn (Technische Universität München), Horng-Tzer Yau (Harvard University)

The past decade has seen tremendous progress in understanding the behavior of large random matrices and interacting particle systems. Complementary methods have emerged to prove universality of these behaviors, as well as to probe their precise nature using integrable, or exactly solvable models. This program seeks to reinforce and expand the fruitful interaction at the interface of these areas, as well as to showcase some of the important developments and applications of the past decade.

Updated on Aug 31, 2021 03:05 PM PDT
4. # ProgramComplementary Program 2021-22

The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program.

Updated on Jan 15, 2021 11:53 AM PST
1. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
2. # SeminarMini-Course: Introduction to Fluctuations of Beta-Ensembles

Updated on Oct 22, 2021 08:17 AM PDT
3. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
4. # SeminarPositivity and Universality (from a Combinatorial Perspective)

Updated on Oct 21, 2021 09:24 AM PDT
5. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:21 PM PDT
6. # SeminarFellowship of the Ring: Support Theories for Non-Commutative Complete Intersections

Updated on Oct 20, 2021 11:40 AM PDT
7. # SeminarMini-Course: The Quest for Fredholm Determinants

Updated on Oct 19, 2021 02:58 PM PDT
8. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
9. # Seminar Mini-Course: Introduction to Fluctuations of Beta-Ensembles

Updated on Oct 22, 2021 08:18 AM PDT
10. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
11. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:22 PM PDT
12. # SeminarMini-Course: The Quest for Fredholm Determinants

Updated on Oct 19, 2021 03:28 PM PDT
13. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
14. # SeminarLongest Increasing Subsequence and the Schensted Shape of Some Pseudo-Random Sequences

Updated on Oct 20, 2021 02:30 PM PDT
15. # SeminarProgram Associates' Seminar: an Introduction to Duality

Updated on Oct 22, 2021 03:17 PM PDT
16. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
17. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
18. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
19. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:22 PM PDT
20. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
21. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
22. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:23 PM PDT
23. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
24. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
25. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
26. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
27. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:23 PM PDT
28. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
29. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
30. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
31. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
32. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
33. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
34. # WorkshopChern-Simons and Other Topological Field Theories

Organizers: Stephon Alexander (Brown University), Fiona Burnell (University of Minnesota), David Eisenbud (MSRI - Mathematical Sciences Research Institute), Dan Freed (University of Texas, Austin), Joel Moore (University of California, Berkeley), John Morgan (Columbia University)

The introduction of the Chern-Simons differential form in 1972 catalyzed a remarkable series of developments across mathematics and physics, continuing to the present day.

The classical Chern-Simons invariant provides an obstruction to immersing a 3-manifold conformally into Euclidean 4-space, while the quantum Chern-Simons invariants in topological field theories gave rise to many new developments in knot theory.  In physics, the Chern-Simons action for gauge fields is widely discussed as an alternative or supplement to conventional Maxwell and Einstein theories. Topological field theories encode the fractional statistics of emergent anyon particles in condensed matter.

This workshop will cover the current state of the manifold areas in mathematics and physics in which Chern-Simons and other topological field theories have had a dramatic impact, as well as their appearance in new areas ranging from integrability to number theory.

Shiing-Shen Chern, the founding Director of MSRI was born on October 28, 1911 in Jiaxing, China. We join the Chern Institute of Mathematics at Nankai University and the Yau Mathematical Sciences Center at Tsinghua University in celebrating Professor Chern's 110th Birthday, following Chinese tradition.

Updated on Sep 24, 2021 11:27 AM PDT
35. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:23 PM PDT
36. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
37. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
38. # WorkshopBlackwell Tapia Conference 2021

Organizers: David Banks (Duke University), Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), Lloyd Douglas, Robert Megginson (University of Michigan), Mariel Vazquez (University of California, Davis), Ulrica Wilson (Morehouse College; Institute for Computational and Experimental Research in Mathematics (ICERM))

MSRI and the Mathematical Science Institutes Diversity Initiative (MSIDI) are pleased to announce that the 2021 Blackwell-Tapia Conference (rescheduled from Fall 2020), will be held simultaneously at four locations nationwide.  The conference will celebrate the 2020 Blackwell-Tapia prize winner, Tatiana Toro (University of Washington), who has recently been announced as the next Director of MSRI, effective August 2022.

Choose from four host sites nationwide:

Mathematical Sciences Research Institute (MSRI): Berkeley, California
Institute for Pure and Applied Mathematics (IPAM): Los Angeles, California
Institute for Mathematical and Statistical Innovation (IMSI): Chicago, Illinois
Institute for Advanced Study (IAS): Princeton, New Jersey

Updated on Sep 02, 2021 08:26 AM PDT
39. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:23 PM PDT
40. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
41. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
42. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
43. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
44. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:24 PM PDT
45. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
46. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
47. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
48. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
49. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:24 PM PDT
50. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
51. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
52. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:24 PM PDT
53. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
54. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
55. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
56. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
57. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
58. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
59. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
60. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
61. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
62. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
63. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
64. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
65. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
66. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
67. # SeminarThe Analysis and Geometry of Random Spaces - Virtual Participant

Updated on Apr 07, 2021 10:48 AM PDT
68. # SeminarComplex Dynamics: from special families to natural generalizations in one and several variables - Virtual Participant

Updated on Apr 07, 2021 10:49 AM PDT
69. # ProgramThe Analysis and Geometry of Random Spaces

Organizers: LEAD Mario Bonk (University of California, Los Angeles), Joan Lind (University of Tennessee), Steffen Rohde (University of Washington), Eero Saksman (University of Helsinki), Fredrik Viklund (Royal Institute of Technology), Jang-Mei Wu (University of Illinois at Urbana-Champaign)

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers,  random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

Updated on Nov 20, 2019 02:12 PM PST
70. # ProgramComplex Dynamics: from special families to natural generalizations in one and several variables

Organizers: LEAD Sarah Koch (University of Michigan), Jasmin Raissy (Institut de Mathématiques de Bordeaux), Dierk Schleicher (Université d'Aix-Marseille (AMU)), Mitsuhiro Shishikura (Kyoto University), Dylan Thurston (Indiana University)
The mating of these two dendritic Julia sets is equal to the Julia set of a rational map of degree 2; that Julia set is equal to the entire Riemann sphere. Picture by Arnaud Chéritat

Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond.

Our semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. We will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics.

Updated on Nov 20, 2019 02:12 PM PST
71. # WorkshopConnections Workshop: The Analysis and Geometry of Random Spaces

Organizers: Mario Bonk (University of California, Los Angeles), LEAD Joan Lind (University of Tennessee), Eero Saksman (University of Helsinki), Jang-Mei Wu (University of Illinois at Urbana-Champaign)
Simulation of the discrete planar Gaussian free field. Image by Dr. Ellen Powell.

The Connections Workshop will feature talks on a variety of topics related to the analysis and geometry of random spaces. It will preview the research themes of the semester program and will highlight the work of women in the field. There will be a panel discussion as well as other social events. This workshop is directly prior to the Introductory Workshop, and participants are encouraged to participate in both workshops. This workshop is open to all mathematicians.

Updated on Mar 25, 2021 09:38 AM PDT
72. # WorkshopIntroductory Workshop: The Analysis and Geometry of Random Spaces

Organizers: LEAD Mario Bonk (University of California, Los Angeles), Joan Lind (University of Tennessee), Steffen Rohde (University of Washington), Fredrik Viklund (Royal Institute of Technology)
Interface for the critical Ising model, approaching an SLE curve in the scaling limit (image by Dr. Malin P. Forsström)

This workshop will introduce some of the major themes in probability and geometric analysis that will be relevant for the semester-long program. A series of short mini-courses will give participants the opportunity to learn about important subjects such as the Schramm-Loewner evolution (SLE) or the Gaussian free field (GFF), for example. The workshop will also include "visionary" lectures by prominent researchers who will outline fruitful directions for future research.

Updated on Oct 06, 2021 08:33 AM PDT
73. # WorkshopConnections Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables

Organizers: Núria Fagella (University of Barcelona), LEAD Tanya Firsova (Kansas State University), Thomas Gauthier (École Polytechnique), Sarah Koch (University of Michigan)

This workshop will feature lectures on a variety of topics in complex dynamics, given by prominent researchers in the field, as well as presentations by younger participants. It precedes the introductory workshop and will preview the major research themes of the semester program. There will be a panel discussion focusing on issues particularly relevant to junior researchers, women, and minorities, as well as other social events. This workshop is open to all mathematicians.

Updated on Oct 11, 2021 01:43 PM PDT
74. # WorkshopIntroductory Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables

Organizers: Anna Miriam Benini (Università di Parma), Fabrizio Bianchi (Université de Lille), Mikhail Hlushchanka (Universiteit Utrecht), LEAD Dylan Thurston (Indiana University)
Parameter space for the family $e^z+c$

This workshop is built around four minicourses that will introduce the participants to a range of recent techniques in various areas of holomorphic dynamics, given by specialists in these topics. The event is complemented by a series of talks by leaders in the field, aimed at a large audience and presenting current research directions in the area.

Updated on Apr 29, 2021 04:22 PM PDT
75. # WorkshopHot Topics: Foundations of Stable, Generalizable and Transferable Statistical Learning

Organizers: LEAD Peter Bühlmann (ETH Zurich), John Duchi (Stanford University), Elizabeth Tipton (Northwestern University), Bin Yu (University of California, Berkeley)
When data automatically drop from the sky: intelligent approaches in data science change the way humans and computers interact. (Illustration: Niklas Briner)

Despite the remarkable success in extracting information from complex and (often) large-scale datasets over the last two decades, further progress is needed to making automated statistical and machine learning algorithms more reliable, robust, interpretable and trustworthy. This workshop has its focus on foundational aspects of this goal, linking areas at the interface between statistics, optimization, machine learning and computer science, such as distributional robustness and stability, adversarial and transfer learning, generalizability and meta analysis, and causality.

Updated on Sep 23, 2021 09:42 AM PDT
76. # WorkshopHot Topics: Regularity Theory for Minimal Surfaces and Mean Curvature Flow

Organizers: Christine Breiner (Fordham University), Otis Chodosh (Stanford University), Luca Spolaor (University of California, San Diego), Lu Wang (Yale University)

This workshop will explore connections between the regularity theory of minimal surfaces and of mean curvature flow. Recent breakthroughs have improved our understanding of singularity formation in both settings but the current research trends are becoming increasingly disparate. Experts from both areas will present their research and there will be ample free time to establish connections between the topics.

Updated on Oct 13, 2021 08:42 AM PDT
77. # WorkshopThe Analysis and Geometry of Random Spaces

Organizers: Nikolai Makarov (California Institute of Technology), LEAD Steffen Rohde (University of Washington), Eero Saksman (University of Helsinki), Amanda Turner (University of Lancaster), Fredrik Viklund (Royal Institute of Technology), Jang-Mei Wu (University of Illinois at Urbana-Champaign)
Image by Prof. Amanda Turner

The aim of this workshop is to bring together researchers whose work contributes to the study of random structures that exhibit some form of conformal self-similarity. Notable examples include the Schramm-Loewner evolution SLE, the Brownian map and random trees, Liouville Quantum Gravity, and Conformal Field Theory. A particular focus will be the discussion of analytic tools needed to address the challenges arising from the often rough underlying sets and spaces.

Updated on Oct 11, 2021 01:11 PM PDT
78. # WorkshopAdventurous Berkeley Complex Dynamics

Organizers: Mikhail Lyubich (State University of New York, Stony Brook), LEAD Jasmin Raissy (Institut de Mathématiques de Bordeaux), LEAD Roland Roeder (Indiana University--Purdue University), Dierk Schleicher (Université d'Aix-Marseille (AMU))
Image by Scott Kaschner

This workshop will focus on complex dynamics in one and several variables. We will bring toghether experts in rational dynamics, transcendental dynamics, and dynamics in several complex variables in order to get new perspective and foster discussions in a warm and stimulating atmosphere. A special focus will be put on the interactions between one dimensional and higher dimensional complex dynamics, and on connections with adjacent areas of mathematics.

Updated on Feb 10, 2021 08:38 AM PST
79. # Summer Research in Mathematics2022 Summer Research in Mathematics

MSRI's Summer Research in Mathematics program provides space, funding, and the opportunity for in-person collaboration to small groups of mathematicians, especially women and gender-expansive individuals, whose ongoing research may have been disproportionately affected by various obstacles including family obligations, professional isolation, or access to funding. Through this effort, MSRI aims to mitigate the obstacles faced by these groups, improve the odds of research project completion, and deepen their research experience.

The ultimate goal of this program is to enhance the mathematical sciences as a whole by positively affecting the research and careers of all of its participants and assisting their efforts to maintain involvement in the research community.

Updated on Sep 15, 2021 09:26 AM PDT
80. # Summer Graduate SchoolIntegral Equations and Applications

Organizers: Fioralba Cakoni (Rutgers University), Dorina Mitrea (Baylor University), Irina Mitrea (Temple University), Shari Moskow (Drexel University)
L 2 Spectra of K for apertures π 15 , · · · 14π 15 , π

The field of Integral Equations has a long and distinguished history, being the driving force behind many fundamental developments in various areas of mathematics including Harmonic Analysis, Partial Differential Equations, Potential Theory, Scattering Theory, Functional Analysis, Complex Analysis, Operator Theory, Mathematical Physics and Numerical Analysis.

This school will:

1. introduce graduate students to the systematic study of integral equations;
2. present some of the latest theoretical advancements in the field and open problems; and
3. involve participants in a hands-on discovery lab focused on deriving results about integral operators in two dimensions relevant for both the theoretical and numerical treatment of Integral Equations in two dimensions. The curriculum of this program will be accessible and will have a broad appeal to graduate students from a variety of mathematical areas (both theoretical and applied).

Updated on Sep 02, 2021 04:19 PM PDT
81. # MSRI-UPMSRI-UP 2022: Algebraic Methods in Mathematical Biology

Organizers: LEAD Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI - Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), Candice Price (Smith College), Anne Shiu (Texas A & M University)

The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

In 2022, MSRI-UP will focus on Algebraic Methods in Mathematical Biology. The research program will be led by Dr. Anne Shiu, Associate Professor of Mathematics at Texas A&M University.

Updated on Aug 25, 2021 03:37 PM PDT
82. # African Diaspora Joint Mathematics2022 African Diaspora Joint Mathematics Workshop

The African Diaspora Joint Mathematics Workshop (ADJOINT) is a yearlong program that provides opportunities for U.S. mathematicians – especially those from the African Diaspora – to form collaborations with distinguished African-American research leaders on topics at the forefront of mathematical and statistical research.

Beginning with an intensive two-week summer session at MSRI, participants work in small groups under the guidance of some of the nation’s foremost mathematicians and statisticians to expand their research portfolios into new areas. Throughout the following academic year, the program provides conference and travel support to increase opportunities for collaboration, maximize researcher visibility, and engender a sense of community among participants. The 2022 program takes place June 20 - July 1, 2022 in Berkeley, California.

Updated on Oct 13, 2021 03:27 PM PDT
83. # Summer Graduate SchoolNew Directions in Representation Theory (AMSI, Brisbane, Australia)

Organizers: Angela Coughlin (Australian Mathematical Sciences Institute), Joseph Grotowski (University of Queensland), Tim Marchant (Australian Mathematical Sciences Institute), Ole Warnaar (University of Queensland), Geordie Williamson (University of Sydney)

Representation Theory has undergone a revolution in recent years, with the development of what is now known as higher representation theory. In particular, the notion of categorification has led to the resolution of many problems previously considered to be intractable.

The school will begin by providing students with a brief but thorough introduction to what could be termed the “bread and butter of modern representation theory”, i.e., compact Lie groups and their representation theory; character theory; structure theory of algebraic groups.

We will then continue on to a number of more specialized topics. The final mix will depend on discussions with the prospective lecturers, but we envisage such topics as:

• modular representation theory of finite groups (blocks, defect groups, Broué’s conjecture);

• perverse sheaves and the geometric Satake correspondence;

• the representation theory of real Lie groups.

Updated on Sep 03, 2021 09:18 AM PDT
84. # Summer Graduate SchoolGeometric Flows (Athens, Greece)

Organizers: Nicholas Alikakos (National and Kapodistrian University of Athens (University of Athens)), Panagiota Daskalopoulos (Columbia University)

[The image on this vase from Minoan Crete, dated on 1500-2000 BC, resembles an ancient solution to the Curve shortening flow - one of the most basic geometric flows. The vase is at Heraklion Archaeological Museum]

This summer graduate school is a collaboration between MSRI and the FORTH-IACM Institute in Crete. The purpose of the school is to introduce graduate students to some of the most important geometric evolution equations. Information about the location of the summer school can be found here.

This is an area of geometric analysis that lies at the interface of differential geometry and partial differential equations. The lectures will begin with an introduction to nonlinear diffusion equations and continue with classical results on the Ricci Flow, the  Mean curvature flow and other fully non-linear extrinsic flows such as the Gauss curvature flow. The lectures will also include geometric applications such as isoperimetric inequalities, topological applications such as the Poincaré onjecture, as well as recent important developments related to the study of singularities and ancient solutions.

Updated on Sep 03, 2021 09:08 AM PDT
85. # Summer Graduate SchoolRandom Graphs

Organizers: Louigi Addario-Berry (McGill University), Remco van der Hofstad (Technische Universiteit Eindhoven)
by DeDelphin Sénizergues

The topic of random graphs is at the forefront of applied probability, and it is one of the central topics in multidisciplinary science where mathematical ideas are used to model and understand the real world. At the same time, random graphs pose challenging mathematical problems that have attracted the attention from probabilists and combinatorialists since the 1960, with the pioneering work of Erdös and Rényi. Around the turn of the millennium, very large data sets started to become available, and several applied disciplines started to realize that many real-world networks, even though they are from various different origins, share many fascinating features. In particular, many of such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scalefree, in the sense that there are enormous differences in the number of connections that their elements make. In particular, such networks are quite different from the classical random graph models, such as proposed by Erdös and Rényi.

Updated on Sep 02, 2021 04:21 PM PDT
86. # Summer Graduate SchoolAlgebraic Theory of Differential and Difference Equations, Model Theory and their Applications

Organizers: LEAD Alexey Ovchinnikov (Queens College, CUNY), Anand Pillay (University of Notre Dame), Thomas Scanlon (University of California, Berkeley), Michael Wibmer (University of Notre Dame)
Algebraic Theory Of Differential And Difference Equations, Model Theory And Their Applications

The purpose of the summer school will be to introduce graduate students to effective methods in algebraic theories of differential and difference equations with emphasis on their model-theoretic foundations and to demonstrate recent applications of these techniques to studying dynamic models arising in sciences. While these topics comprise a coherent and rich subject, they appear in graduate coursework in at best a piecemeal way, and then only as components of classes for other aims. With this Summer Graduate School, students will learn both the theoretical basis of differential and difference algebra and how to use these methods to solve practical problems. Beyond the lectures, the graduate students will meet daily in problem sessions and will participate in one-on-one mentoring sessions with the lecturers and organizers.

Updated on Sep 02, 2021 04:25 PM PDT
87. # Summer Graduate SchoolMetric Geometry and Geometric Analysis (Oxford, United Kingdom)

Organizers: LEAD Cornelia Drutu (University of Oxford), Panos Papazoglou (University of Oxford)

The purpose of the summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of non-smooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.

All these themes are intertwined and have developed either together or greatly influencing one another. The summer school will introduce some of the latest developments and the remaining open problems in these very modern areas, and will emphasize their synergy.

Updated on Sep 02, 2021 12:26 PM PDT
88. # Summer Graduate SchoolSéminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory

Organizers: Kristen Hendricks (Rutgers University), Ailsa Keating (University of Cambridge), Robert Lipshitz (University of Oregon), Liam Watson (University of British Columbia), Ben Williams (University of British Columbia)
Image by Prof. Robert Lipshitz

The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg--Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.

The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.

Updated on Sep 10, 2021 11:11 AM PDT
89. # Summer Graduate School2022 Joint PCMI School: Number Theory Informed by Computation

Organizers: Jennifer Balakrishnan (Boston University), Rafe Mazzeo (Stanford University), Bjorn Poonen (Massachusetts Institute of Technology), Akshay Venkatesh (Institute for Advanced Study)

The PCMI graduate summer school program in 2022 will consist of a sequence of 11 minicourses. The lecturers and topics for these minicourses are listed below. Each minicourse is accompanied by a problem session. The topics are arranged so that there is good material and opportunities for learning both for less experienced students as well as more advanced students. Beyond their attendance in these minicourse sessions, all graduate participants will be able to take part in the substantial other benefits of a PCMI session. This includes the opportunity to interact with the researchers in residence and take part in the research seminar component of PCMI. Many graduate students also interact in significant ways with the undergraduate cohort,,the undergraduate faculty cohort, and may also participate in the many pedagogically focused activities which form part of the K-12 Teacher Leadership Program and the Workshop for Equity in Mathematics Education. PCMI includes numerous cross-program activities to help members from all these groups interact with one another.

Updated on Sep 16, 2021 03:02 PM PDT
90. # Summer Graduate SchoolMathematics of Machine Learning (INdAM Joint School 2021)

Organizers: Sebastien Bubeck (Microsoft Research), Anna Karlin (University of Washington), Adith Swaminathan (Microsoft Research)
Popular visualization of the MNIST dataset

Dates listed are a placeholder.  Actual dates are to be determined.

Learning theory is a rich field at the intersection of statistics, probability, computer science, and optimization. Over the last decades the statistical learning approach has been successfully applied to many problems of great interest, such as bioinformatics, computer vision, speech processing, robotics, and information retrieval. These impressive successes relied crucially on the mathematical foundation of statistical learning.

Recently, deep neural networks have demonstrated stunning empirical results across many applications like vision, natural language processing, and reinforcement learning. The field is now booming with new mathematical problems, and in particular, the challenge of providing theoretical foundations for deep learning techniques is still largely open. On the other hand, learning theory already has a rich history, with many beautiful connections to various areas of mathematics (e.g., probability theory, high dimensional geometry, game theory). The purpose of the summer school is to introduce graduate students (and advanced undergraduates) to these foundational results, as well as to expose them to the new and exciting modern challenges that arise in deep learning and reinforcement learning.

Updated on Sep 03, 2021 11:31 AM PDT
91. # Summer Graduate SchoolRecent Topics in Well Posedness (Taipei, Taiwan)

Organizers: Jungkai Chen (National Taiwan University), Yoshikazu Giga (University of Tokyo), Maria Schonbek (University of California, Santa Cruz), Tsuyoshi Yoneda (University of Tokyo)
Fluid-flow stream function color-coded by vorticity in 3D flat torus calculated by K. Nakai (The University of Tokyo)

The purpose of the workshop is to introduce graduate students to fundamental results on the Navier-Stokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.

Updated on Sep 02, 2021 04:27 PM PDT
92. # Summer Graduate SchoolTopological Methods for the Discrete Mathematician

Organizers: Pavle Blagojevic (Freie Universität Berlin), Florian Frick (Carnegie Mellon University), Shira Zerbib (Iowa State University)

Recently, progress in the field of topological methods in discrete mathematics has been rapid and has generated a lot of activity with the resolution of major open problems, the emergence of new lines of inquiry, and the development of new tools. These exciting new developments have not been digested into a textbook treatment. The two main goals of this school are to:

1. Provide graduate students with a thorough introduction to novel topological techniques and to a handful of their applications in the fields of combinatorics and discrete geometry with short glimpses into mathematical mechanics and algorithm complexity.
2. Expose students to current research, and guide them in research on open problems in discrete mathematics using modern topological tools.

The summer school will lead participants from appealing, simple-to-state problems at confluence of combinatorics, geometry, and topology to sophisticated topological methods that are required for their resolution. In recent years topological methods have found numerous novel applications in mathematics and beyond, such as in data science, machine learning, economics, the social sciences, and biology.  The problems we will discuss are particularly well-suited to rapidly put students in a position to approach related research questions.

Updated on Sep 07, 2021 09:52 AM PDT
93. # ProgramOffsite Simons Postdoctoral Fellowship 2022/23

Updated on Aug 03, 2021 01:30 PM PDT
94. # Summer Graduate School Sums of Squares Method in Geometry, Combinatorics and Optimization

Organizers: LEAD Grigoriy Blekherman (Georgia Institute of Technology), Annie Raymond (University of Massachusetts Amherst), Rekha Thomas (University of Washington)
Graph of the Motzkin polynomial, which is nonnegative but not a sum of squares.

The study of nonnegative polynomials and sums of squares is a classical area of real algebraic geometry dating back to Hilbert’s 17th problem. It also has rich connections to real analysis via duality and moment problems. In the last 15 years, sums of squares relaxations have found a wide array of applications from very applied areas (e.g., robotics, computer vision, and machine learning) to theoretical applications (e.g., extremal combinatorics, theoretical computer science). Also, an intimate connection between sums of squares and classical algebraic geometry has been found. Work in this area requires a blend of ideas and techniques from algebraic geometry, convex geometry and representation theory. After an introduction to nonnegative polynomials, sums of squares and semidefinite optimization, we will focus on the following three topics:

• Sums of squares on real varieties (sets defined by real polynomial equations) and connections with classical algebraic geometry.
• Sums of squares method for proving graph density inequalities in extremal combinatorics. Here addition and multiplication take place in the gluing algebra of partially labelled graphs.
• Sums of squares relaxations for convex hulls of real varieties and theta-bodies with applications in optimization.

The summer school will give a self-contained introduction aimed at beginning graduate students, and introduce participants to the latest developments. In addition to attending the lectures, students will meet in intensive problem and discussion sessions that will explore and extend the topics developed in the lectures.

Updated on Sep 02, 2021 04:23 PM PDT
95. # Summer Graduate SchoolTropical Geometry

Organizers: Renzo Cavalieri (Colorado State University), Hannah Markwig (Eberhard-Karls-Universität Tübingen), Dhruv Ranganathan (University of Cambridge)
A tropical stable map and the corresponding floor diagram

Enumerative geometry and the theory of moduli spaces of curves are two cornerstones of modern algebraic geometry; the two subjects have had a significant influence on each other. In the last 15 years, discrete and combinatorial methods, systematized within tropical geometry, have begun to provide new avenues of access into these two subjects. The goal of this summer school is to give students crash courses in tropical and logarithmic geometry, with a particular focus on the applications in enumerative geometry and moduli theory.  The school will consist of three courses of seven lectures each:

1. Enumeration of tropical curves/ by Hannah Markwig
2. Curve counting in tropical and algebraic geometry by Renzo Cavalieri
3. Logarithmic geometry and stable map/s by Dhruv Ranganathan

Updated on Sep 02, 2021 04:26 PM PDT
96. # ProgramFloer Homotopy Theory

Organizers: Mohammed Abouzaid (Columbia University), Andrew Blumberg (Columbia University), Kristen Hendricks (Rutgers University), Robert Lipshitz (University of Oregon), LEAD Ciprian Manolescu (Stanford University), Nathalie Wahl (University of Copenhagen)
Illustrated by Nathalie Wahl

The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes.  In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and low-dimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory.

Updated on Oct 02, 2020 03:01 PM PDT
97. # ProgramAnalytic and Geometric Aspects of Gauge Theory

Organizers: Laura Fredrickson (University of Oregon), Rafe Mazzeo (Stanford University), Tomasz Mrowka (Massachusetts Institute of Technology), Laura Schaposnik (University of Illinois at Chicago), LEAD Thomas Walpuski (Humboldt-Universität)

The mathematics and physics around gauge theory have, since their first interaction in the mid 1970’s, prompted tremendous developments in both mathematics and physics.  Deep and fundamental tools in partial differential equations have been developed to provide rigorous foundations for the mathematical study of gauge theories.  This led to ongoing revolutions in the understanding of manifolds of dimensions 3 and 4 and presaged the development of symplectic topology.  Ideas from quantum field theory have provided deep insights into new directions and conjectures on the structure of gauge theories and suggested many potential applications.  The focus of this program will be those parts of gauge theory which hold promise for new applications to geometry and topology and require development of new analytic tools for their study.

Updated on Oct 28, 2020 09:12 AM PDT
98. # WorkshopConnections Workshop: Analytic and Geometric Aspects of Gauge Theory

Organizers: Lara Anderson (Virginia Polytechnic Institute and State University), Casey Kelleher (Princeton University), LEAD Laura Schaposnik (University of Illinois at Chicago)
The nilpotent cone in red over the 0, and the points A, B and C, lying over the C*-fow and of the Hitchin section respectively.

This two-day workshop will consist of various talks given by prominent female mathematicians on topics of analytic and geometric aspects of gauge theory. These will be appropriate for graduate students, post-docs, and researchers in areas related to the program.  The meeting aims to support young researchers working in analytic and geometric aspects of gauge theory by   facilitating mentoring from senior colleagues and helping towards the development of crucial professional skills. The format will include mentoring pairings, panel discussions, and Q&A sessions as well as the opportunity for informal discussions and connections.

Updated on Mar 22, 2021 09:08 AM PDT
99. # WorkshopIntroductory Workshop: Analytic and Geometric Aspects of Gauge Theory

Organizers: LEAD Aleksander Doan (State University of New York, Stony Brook), Laura Fredrickson (University of Oregon), Michael Singer (University College London)
Portion of a letter from Maxwell to Tait dated December 4, 1867 computing the linking number of two curves

The workshop will highlight the utility and impact of gauge theory in other areas of math. Mini-courses will cover the historical utility and impact of gauge theory in areas including low-dimensional topology, algebraic geometry, and the analysis of PDE; additional talks will cover more recent directions.

Updated on May 03, 2021 10:23 AM PDT
100. # WorkshopConnections Workshop: Floer Homotopy Theory

Organizers: Teena Gerhardt (Michigan State University), LEAD Kristen Hendricks (Rutgers University), Ailsa Keating (University of Cambridge)
An illustration of a generic Heegaard quadruple by K. Hendricks, J. Hom, M. Stoffregen, and I. Zemke

This workshop will feature talks by experts in Floer theory (and its applications to low-dimensional topology) and homotopy theory. It will include two expository lectures aimed at graduate students and other researchers who are new to the field, as well as a sequence of research talks and a contributed talks session. There will also be a panel discussion focusing on professional development. The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.

Updated on Aug 25, 2021 02:03 PM PDT
101. # WorkshopIntroductory Workshop: Floer Homotopy Theory

Organizers: Sheel Ganatra (University of Southern California), Tyler Lawson (University of Minnesota Twin Cities), LEAD Robert Lipshitz (University of Oregon), Nathalie Wahl (University of Copenhagen)
A Fleur Homotopy.

Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications.

Updated on Mar 10, 2021 09:12 AM PST
102. # WorkshopNew four-dimensional gauge theories

Organizers: Andriy Haydys (Albert-Ludwigs-Universität Freiburg), Lotte Hollands (Heriot-Watt University, Riccarton Campus), LEAD Eleny-Nicoleta Ionel (Stanford University), Richard Thomas (Imperial College, London), Thomas Walpuski (Humboldt-Universität)
Image drawn by Dr. Lotte Hollands

This workshop will bring together researchers working on new four-dimensional gauge theories from the perspectives of differential geometry, algebraic geometry, and physics. Over the last 25 years, physicists have made tantalizing conjectures relating the Vafa–Witten equation to modular forms and the Kapustin–Witten and Haydys–Witten equations to knot theory and the geometric Langlands programme. The analytical challenges in the way of establishing these predictions are now being pursued vigorously.  More recently, algebraic geometers have had enormous success in confirming and refining Vafa–Witten's predictions for projective surfaces. The workshop will serve as a platform for reporting on recent progress and exchanging ideas in all of these areas, with the aim of strengthening existing and fostering new interactions.

Created on Mar 18, 2021 02:28 PM PDT
103. # WorkshopFloer homotopical methods in low dimensional and symplectic topology

Organizers: LEAD Mohammed Abouzaid (Columbia University), Andrew Blumberg (Columbia University), Jennifer Hom (Georgia Institute of Technology), Emmy Murphy (Northwestern University), Sucharit Sarkar (University of California, Los Angeles)

The workshop will focus on the interaction between homotopy theory and symplectic topology and low dimensional topology that is mediated by Floer theory. Among the topics covered are foundational questions, applications to concrete geometric questions, and the relationship with finite dimensional approaches.

Updated on Mar 18, 2021 02:21 PM PDT
104. # ProgramAlgebraic Cycles, L-Values, and Euler Systems

Organizers: Henri Darmon (McGill University), Ellen Eischen (University of Oregon), LEAD Benjamin Howard (Boston College), David Loeffler (University of Warwick), Christopher Skinner (Princeton University), Sarah Zerbes (University College London), Wei Zhang (Massachusetts Institute of Technology)
Some Gaussian periods for the 255,255-th cyclotomic extension. Image credit: E. Eischen, based on earlier work by W. Duke, S. R. Garcia, T. Hyde, and R. Lutz

The fundamental conjecture of Birch and Swinnerton-Dyer relating the Mordell–Weil ranks of elliptic curves to their L-functions is one of the most important and motivating problems in number theory. It resides at the heart of a collection of important conjectures (due especially to Deligne, Beilinson, Bloch and Kato) that connect values of L-functions and their leading terms to cycles and Galois cohomology groups.

The study of special algebraic cycles on Shimura varieties has led to progress in our understanding of these conjectures. The arithmetic intersection numbers and the p-adic regulators of special cycles are directly related to the values and derivatives of L-functions, as shown in the pioneering theorem of Gross-Zagier and its p-adic avatars for Heegner points on modular curves. The cohomology classes of special cycles (and related constructions such as Eisenstein classes) form the foundation of the theory of Euler systems, providing one of the most powerful methods known to prove vanishing or finiteness results for Selmer groups of Galois representations.

The goal of this semester is to bring together researchers working on different aspects of this young but fast-developing subject, and to make progress on understanding the mysterious relations between L-functions, Euler systems, and algebraic cycles.

Updated on Apr 12, 2021 10:17 AM PDT
105. # ProgramDiophantine Geometry

Organizers: Jennifer Balakrishnan (Boston University), Mirela Ciperiani (University of Texas, Austin), Philipp Habegger (University of Basel), Wei Ho (University of Michigan), LEAD Hector Pasten (Pontificia Universidad Católica de Chile), Yunqing Tang (Princeton University), Shou-Wu Zhang (Princeton University)
A rational point on a curve of genus 3

While the study of rational solutions of diophantine equations initiated thousands of years ago, our knowledge on this subject has dramatically improved in recent years. Especially, we have witnessed spectacular progress in aspects such as height formulas and height bounds for algebraic points, automorphic methods, unlikely intersection problems, and non-abelian and p-adic approaches to algebraic degeneracy of rational points. All these groundbreaking advances in the study of rational and algebraic points in varieties will be the central theme of the semester program “Diophantine Geometry” at MSRI. The main purpose of this program is to bring together experts as well as enthusiastic young researchers to learn from each other, to initiate and continue collaborations, to update on recent breakthroughs, and to further advance the field by making progress on fundamental open problems and by developing further connections with other branches of mathematics. We trust that younger mathematicians will greatly contribute to the success of the program with their new ideas. It is our hope that this program will provide a unique opportunity for women and underrepresented groups to make outstanding contributions to the field, and we strongly encourage their participation.

Updated on Feb 25, 2021 04:59 PM PST
106. # WorkshopConnections Workshop: Algebraic Cycles, L-Values, and Euler Systems

Organizers: Henri Darmon (McGill University), Ellen Eischen (University of Oregon), Benjamin Howard (Boston College), LEAD Elena Mantovan (California Institute of Technology)
David Lowry-Duda. Modular form of weight 32 and level 3. For details, see http://davidlowryduda.com/trace-form/

The Connections Workshop features presentations by both leading researchers and promising newcomers whose research has contact with the interrelated topics of algebraic cycles, L-values, and Euler systems. The goal is to present a variety of diverse results, so as to forge new connections, foster collaborative projects, and establish mentoring relationships. While emphasis will be placed on the work of women mathematicians, the workshop is open to all researchers.

Updated on Apr 09, 2021 09:14 AM PDT
107. # WorkshopIntroductory Workshop: Algebraic Cycles, L-Values, and Euler Systems

Organizers: Henri Darmon (McGill University), LEAD Ellen Eischen (University of Oregon), Benjamin Howard (Boston College), Elena Mantovan (California Institute of Technology)
Image credit: Vincent J. Matsko, 6-adic Koch-like fractal. For details, see http://www.vincematsko.com/Art/ICERM.html

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research.

Updated on Apr 12, 2021 10:18 AM PDT
108. # WorkshopShimura Varieties and L-functions

Organizers: Michael Harris (Columbia University), David Loeffler (University of Warwick), Elena Mantovan (California Institute of Technology), Christopher Skinner (Princeton University), Sarah Zerbes (University College London), LEAD Wei Zhang (Massachusetts Institute of Technology)
Some Gaussian periods for the 29,070-th cyclotomic extension. Image credit: E. Eischen, based on earlier work by W. Duke, S. R. Garcia, T. Hyde, and R. Lutz

The topical workshop will be dedicated to Shouwu Zhang, to mark the occasion of his 60th birthday, and to honour his numerous beautiful contributions to the theory of Shimura varieties and special values of L-functions. It will highlight cutting edge work on topics such as the construction of Euler systems; relations between special cycles on Shimura varieties and L-functions, such as generalized Gross-Zagier formulas and the Tate conjecture; the construction of Galois representations in cohomology; and related aspects of the theory of automorphic forms.

Updated on Aug 25, 2021 03:20 PM PDT
109. # MSRI-UPMSRI-UP 2023

Organizers: Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI - Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), Candice Price (Smith College)

The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

Updated on Sep 16, 2021 09:02 AM PDT
110. # ProgramCommutative Algebra

Organizers: Aldo Conca (Università di Genova), Dale Cutkosky (University of Missouri), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame), Steven Sam (University of California, San Diego), Kevin Tucker (University of Illinois at Chicago), Claire Voisin (Collège de France; Institut de Mathématiques de Jussieu)
Image for theorem about 9 point on cubic curve, the special case of Cayley–Bacharach theorem.

Commutative algebra is, in its essence, the study of algebraic objects, such as rings and modules over them, arising from polynomials and integral numbers.     It has numerous connections to other fields of mathematics including algebraic geometry, algebraic number theory, algebraic topology and algebraic combinatorics. Commutative Algebra has witnessed a number of spectacular developments in recent years, including the resolution of long-standing problems, with new techniques and perspectives leading to an extraordinary transformation in the field. The main focus of the program will be on these developments. These include the recent solution of Hochster's direct summand conjecture in mixed characteristic that employs the theory of perfectoid spaces, a new approach to the Buchsbaum--Eisenbud--Horrocks conjecture on the Betti numbers of modules of finite length, recent progress on the study of Castelnuovo--Mumford regularity, the proof of Stillman's conjecture and ongoing work on its effectiveness, a novel strategy to Green's conjecture on the syzygies of canonical curves based on the study of Koszul modules and their generalizations, new developments in the study of various types of multiplicities, theoretical and computational aspects of Gröbner bases, and the implicitization problem for Rees algebras and its applications.

Updated on Oct 19, 2021 11:00 AM PDT

1. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
2. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
3. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
4. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
5. # Workshop[HYBRID WORKSHOP] Integrable Structures in Random Matrix Theory and Beyond

Organizers: LEAD Jinho Baik (University of Michigan), Alexei Borodin (Massachusetts Institute of Technology), Tamara Grava (University of Bristol; International School for Advanced Studies (SISSA/ISAS)), Alexander Its (Indiana University--Purdue University), Sandrine Peche (Université de Paris VII (Denis Diderot))
Image by Alexei Borodin.

This will be a hybrid workshop with in-person participation by members of the semester-long program. Online participation will be open to all who register.  This workshop will focus on the integrable aspect of random matrix theory and other related probability models such as random tilings, directed polymers, and interacting particle systems. The emphasis is on communicating diverse algebraic structures in these areas which allow the asymptotic analysis possible. Some of such structures are determinantal point processes, Toeplitz and Hankel determinants, Bethe ansatz, Yang-Baxter equation, Karlin-McGregor formula, Macdonald process, and stochastic six vertex model.

Updated on Oct 06, 2021 08:15 AM PDT
6. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
7. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
8. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
9. # SeminarSpectral Theory of Non-Self-Adjoint Dirac Operators on the Circle

Updated on Oct 08, 2021 11:06 AM PDT
10. # SeminarAvoiding Local Parametrix Problems in Riemann-Hilbert Theory

Updated on Oct 08, 2021 12:40 PM PDT
11. # SeminarProgram Associates' Seminar

Updated on Oct 04, 2021 10:56 AM PDT
12. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:17 PM PDT
13. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
14. # SeminarMini-Course: Correlation Functions of the Sinh-Gordon Quantum Field Theory in 1+1 Dimensions Part II

Updated on Oct 13, 2021 10:10 AM PDT
15. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
16. # SeminarIntegrable Probability Open Problem Session

Updated on Oct 04, 2021 10:49 AM PDT
17. # SeminarColloquium: Topological Expansion and Phase Diagram for Ensembles of Random Matrices with Complex Potentials

Updated on Oct 08, 2021 10:27 AM PDT
18. # SeminarIndependence Preserving Transformations and Exact Solvability

Updated on Oct 08, 2021 10:52 AM PDT
19. # SeminarRandom Matrices and Random Landscapes

Updated on Sep 03, 2021 12:15 PM PDT
20. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
21. # SeminarMini-Course: Correlation Functions of the Sinh-Gordon Quantum Field Theory in 1+1 Dimensions Part I

Updated on Oct 13, 2021 10:12 AM PDT
22. # SeminarFellowship of the Ring: The Fiber-Full Scheme

Updated on Oct 11, 2021 01:11 PM PDT
23. # SeminarAfternoon Tea

Updated on Aug 24, 2021 11:21 AM PDT
24. # SeminarWelcome Tea

Updated on Aug 25, 2021 11:32 AM PDT
25. # SeminarProgram Associate Short Talks (3x 25 mins)

Updated on Oct 04, 2021 10:45 AM PDT
26. # SeminarColloquium: A Survey of Results for Asymptotics of Determinants of Operators

Updated on Oct 08, 2021 11:35 AM PDT
There are more then 25 past events. Please go to Past Events to see all past events.