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  1. Program Algebraic 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 (ETH Zürich), 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 Jan 11, 2023 12:03 PM PST
  2. Program Diophantine Geometry

    Organizers: Jennifer Balakrishnan (Boston University), Mirela Ciperiani (University of Texas, Austin), Philipp Habegger (University of Basel), Wei Ho (Institute for Advanced Study), LEAD Hector Pasten (Pontificia Universidad Católica de Chile), Yunqing Tang (University of California, Berkeley), 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 Jan 11, 2023 03:21 PM PST
  1. Seminar 5 Minute Talks

    Updated on Jan 23, 2023 02:43 PM PST
  2. Seminar 5 Minute Talks

    Updated on Jan 23, 2023 02:43 PM PST
  3. Seminar 5 Minute Talks

    Updated on Jan 26, 2023 10:06 AM PST
  4. Workshop Connections Workshop: Diophantine Geometry

    Organizers: Jennifer Balakrishnan (Boston University), LEAD Yunqing Tang (University of California, Berkeley)

    This will be a hybrid workshop with both in-person and virtual participation.

    This workshop will highlight talks on various aspects of Diophantine Geometry. The goal of the workshop is to bring together researchers at different career stages and of various backgrounds in order to establish new collaborations and mentoring relationships. Although we will showcase the research of mathematicians who identify as women or gender minorities, this workshop is open to all.

    Updated on Jan 28, 2023 03:56 PM PST
  5. Workshop Introductory Workshop: Diophantine Geometry

    Organizers: Hector Pasten (Pontificia Universidad Católica de Chile), Yunqing Tang (University of California, Berkeley), LEAD Shou-Wu Zhang (Princeton University)
    Introd image
    Rational points on a general type surface. Image by Hector Pasten.

    This will be a hybrid workshop with both in-person and virtual participation.

    This workshop will feature expository lectures about  current developments in  Diophantine geometry. This includes  the uniform Mordell—Lang for rational points on curves,  the  Andre—Oort conjecture for special points on Shimura varieties, and effective results via Chabauty method, and related topics in  Arakelov theory, unlikely intersections, arithmetic statistics, arithmetic dynamics, and p-adic Hodge theory.

    Updated on Jan 28, 2023 03:57 PM PST
  6. Seminar Meet the Staff Tea

    Created on Jan 25, 2023 08:14 AM PST
  7. Workshop Shimura 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 (ETH Zürich), 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
  8. Workshop Critical Issues in Mathematics Education 2023: Mentoring for Equity

    Organizers: Pamela Harris (University of Wisconsin-Milwaukee), Abbe Herzig (AHH Consulting), LEAD Aris Winger (Georgia Gwinnett College), Michael Young (Carnegie Mellon University)

    The workshop Critical Issues in Mathematics Education: Mentoring for Equity aims to reach a broad audience of faculty and students in postsecondary mathematical sciences. Participants will learn about the evidence base for effective mentoring, with a focus on culturally responsive mentoring that supports all students and faculty along their mathematical paths. The workshop includes a combination of discussion of research evidence, review and adaptation of practical tools, and explicit training in effective mentoring, including how to bring these tools back to participants’ home institutions. The workshop intertwines objectives of increasing participants’ knowledge of the scholarship on effective mentoring, and engages participants in interactive activities to develop tangible skills as mentors and as mentor-trainers. Participants should come with a growth mindset, prepared to reflect on their experiences as mentors and mentees, and actively contribute to activities that build skills for implementing best mentoring practices.  This workshop will cultivate local and national mentoring communities that bring effective tools and strategies to mentoring, so that mentees can persist and thrive in research, teaching, education, and throughout their education and careers. One focus will be on addressing the individual mentoring needs of all faculty and students, including those who have been historically-marginalized in mathematics education and careers.

    Updated on Dec 07, 2022 04:23 PM PST
  9. Workshop MSRI / SLMath 40th Anniversary Symposium

    Organizers: Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), Charles Fefferman (Princeton University), Dan Freed (University of Texas, Austin), Kristin Lauter (Facebook AI Research (FAIR)), Dusa McDuff (Barnard College), Andrei Okounkov (Columbia University), Tatiana Toro (MSRI - Mathematical Sciences Research Institute)
    Slmath 40th anniversary design

    In 2022-23, SLMath (formerly MSRI) celebrates 40 years of serving the mathematical sciences community through our topic-focused programs and workshops, and the general public via our national and global outreach initiatives. 

    Director Tatiana Toro and Deputy Director Hélène Barcelo invite the community to join us for a symposium to reflect upon these four decades of extraordinary activity.  This celebration will feature special guest speakers, panel discussions and an evening reception.

    This event is free and open to the public. Funding is extremely limited. 

    Updated on Jan 26, 2023 01:40 PM PST
  10. Workshop Degeneracy of algebraic points

    Organizers: Jennifer Balakrishnan (Boston University), LEAD Mirela Ciperiani (University of Texas, Austin), Philipp Habegger (University of Basel), Wei Ho (Institute for Advanced Study), Hector Pasten (Pontificia Universidad Católica de Chile), Yunqing Tang (University of California, Berkeley), Shou-Wu Zhang (Princeton University)
    A genus 2 curve over the reals and various p-adics. Image created by Prof. Jennifer Balakrishnan .

    In recent years, a number of techniques have led to outstanding progress on Lang-Vojta conjectures, such as the Subspace Theorem, p-adic approaches to finiteness, and modular methods. Similarly, spectacular progress has been achieved on unlikely intersection conjectures thanks to new methods and tools, such as height formulas for special points, connections to model theory, refined counting results, and new theorems of Ax-Shanuel type (bi-algebraic geometry). The goal of this workshop is to create the opportunity for these two groups to interact, to share their techniques, to update on the most recent progress, and to attack the outstanding open questions in the field.

    Updated on Jul 27, 2022 09:28 AM PDT
  11. Workshop MIP* = RE and the Connes’ Embedding Problem

    Organizers: Michael Chapman (New York University, Courant Institute), Anand Natarajan (Massachusetts Institute of Technology), William Slofstra (University of Waterloo), John Wright (University of Texas, Austin), Henry Yuen (Columbia University)

    This workshop is about the recent MIP*=RE result from quantum computational complexity, and the resulting resolution of the Connes embedding problem from the theory of von Neumann algebras. MIP*=RE connects the disparate areas of computational complexity theory, quantum information, operator algebras, and approximate representation theory. The aim of this workshop is to bridge this divide, by giving an in-depth exposition of the techniques used in the proof of MIP*=RE, and highlighting perspectives on the MIP*=RE result from operator algebras and approximate representation theory. In particular, this workshop will highlight connections with group stability, something that has not been covered in previous workshops. In addition to increasing understanding of the MIP*=RE proof, we hope that this will open up further applications of the ideas behind MIP*=RE in operator algebras.

    Updated on Jan 13, 2023 10:54 AM PST
  12. Summer Graduate School Commutative Algebra and its Interaction with Algebraic Geometry (Notre Dame)

    Organizers: Steven 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)
    1015 image

    Commutative Algebra has seen an extraordinary development in the last few years. Long standing conjectures have been proven and new connections to different areas of mathematics have been built.This summer graduate school will consist of three mini-courses (5 lectures each) on fundamental topics in commutative algebra that are not covered in the standard courses. Each course will be accompanied by problem sessions focused on research. Five general colloquium-style lectures will be given by invited scholars who will also attend the school and help with afternoon research activities. 

    Updated on Jan 11, 2023 01:36 PM PST
  13. Summer Research in Mathematics Summer Research in Mathematics 2023

    MSRI/SLMath'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/SLMath 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.

    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 Dec 08, 2022 03:59 PM PST
  14. Summer Graduate School Formalization of Mathematics (SLMath)

    Organizers: Jeremy Avigad (Carnegie Mellon University), Heather Macbeth (Fordham University at Lincoln Center), Patrick Massot (Université Paris-Saclay)
    Some basic concepts in mathlib and the dependencies between them

    Computational proof assistants now make it possible to develop global, digital mathematical libraries with theorems that are fully checked by computer. This summer school will introduce students to the new technology and the ideas behind it, and will encourage them to think about the goals and benefits of formalized mathematics. Students will learn to use the Lean interactive proof assistant, and by the end of the session they will be in a position to formalize mathematics on their own, join the Lean community, and contribute to its mathematical library.

    Updated on Nov 03, 2022 12:55 PM PDT
  15. MSRI-UP MSRI-UP 2023: Topological Data Analysis

    Organizers: Federico Ardila (San Francisco State University), LEAD Maria Mercedes Franco (Queensborough Community College (CUNY)), Rebecca Garcia (Sam Houston State University), Jose Perea (Michigan State University), Candice Price (Smith College), Robin Wilson (Loyola Marymount 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 2023, MSRI-UP will focus on Topological Data Analysis. The research program will be led by Dr. Jose Perea, Associate Professor in the Department of Mathematics and the Khoury College of Computer Sciences at Northeastern University.

    Updated on Nov 15, 2022 05:48 PM PST
  16. Summer Graduate School Algebraic Methods for Biochemical Reaction Networks (Leipzig, Germany)

    Organizers: Timo de Wolff (TU Berlin), LEAD Alicia Dickenstein (University of Buenos Aires), Elisenda Feliu (University of Copenhagen)
    2021 sgs biochemical reaction networks leipzig image dickenstein.2019.10.09 %281%29
    A basic enzymatic mechanism

    The aim of the course is to learn how tools from algebraic geometry (in particular, from computational and real algebraic geometry) can be used to analyze standard models in molecular biology. Particularly, these models are key ingredients in the development of Systems and Synthetic biology, two active research areas focusing on understanding, modifying, and implementing the design principles of living systems.

    We will focus on the mathematical aspects of the methods, and exemplify and apply the theory to real networks, thereby introducing the participants to relevant problems and mechanisms in molecular biology. As a counterpart, however, the participants will also see how this field has in the past challenged current methods, mainly in the realm of real algebraic geometry, and has given rise to new general and purely theoretical results on polynomial equations. We will end our lectures with an overview of open questions in both fields.

    Updated on Oct 07, 2022 01:49 PM PDT
  17. African Diaspora Joint Mathematics 2023 African Diaspora Joint Mathematics Workshop

    The African Diaspora Joint Mathematics Workshop (ADJOINT) will take place at the Mathematical Sciences Research Institute in Berkeley, CA from June 19 to June 30, 2023.

    ADJOINT is a two-week summer activity designed for researchers with a Ph.D. degree in the mathematical sciences who are interested in conducting research in a collegial environment.  

    The main objective of ADJOINT is to provide opportunities for in-person research collaboration to U.S. mathematicians, especially those from the African Diaspora, who will work in small groups with research leaders on various research projects. 

    Through this effort, MSRI aims to establish and promote research communities that will foster and strengthen research productivity and career development among its participants. The ADJOINT workshops are designed to catalyze research collaborations, provide support for conferences to increase the visibility of the researchers, and to develop a sense of community among the mathematicians who attend. 

    The end goal of this program is to enhance the mathematical sciences and its community by positively affecting the research and careers of African-American mathematicians and supporting their efforts to achieve full access and engagement in the broader research community. 

    Each summer, three to five research leaders will each propose a research topic to be studied during a two-week workshop.

    During the workshop, each participant will: 

    • conduct research at MSRI within a group of four to five mathematicians under the direction of one of the research leaders 
    • participate in professional enhancement activities provided by the onsite ADJOINT Director 
    • receive funding for two weeks of lodging, meals and incidentals, and one round-trip travel to Berkeley, CA 

    After the two-week workshop, each participant will:

    • have the opportunity to further their research project with the team members including the research leader 
    • have access to funding to attend conference(s) or to meet with other team members to pursue the research project, or to present results 
    • become part of a network of research and career mentors

    Updated on Sep 19, 2022 11:48 AM PDT
  18. Summer Graduate School Séminaire de Mathématiques Supérieures 2023: Periodic and Ergodic Spectral Problems (Montréal, Canada)

    Organizers: Alexander Elgart (Virginia Polytechnic Institute and State University), Vojkan Jaksic (McGill University), Svetlana Jitomirskaya (University of California, Irvine), Ilya Kachkovskiy (Michigan State University), Jean Lagacé (King's College London), Leonid Parnovski (University College London)

    This two week school will focus on spectral theory of periodic, almost-periodic, and random operators.  The main aim of this school is to teach the students who work in one of these areas, methods used in parallel problems, explain the similarities between all these areas and show them the `big picture'.

    Updated on Nov 03, 2022 01:55 PM PDT
  19. Summer Graduate School Mathematics and Computer Science of Market and Mechanism Design (SLMath)

    Organizers: Yannai Gonczarowski (Harvard University), Irene Yuan Lo (Stanford University), Ran Shorrer (Pennsylvania State University), LEAD Inbal Talgam-Cohen (Technion---Israel Institute of Technology)

    This school is associated with an upcoming research program at MSRI under the same title. The goal of the school is to equip students unfamiliar with these topics with the mathematical and theoretical computer science toolbox that forms the foundation of market and mechanism design.

    Updated on Nov 03, 2022 11:58 AM PDT
  20. Summer Graduate School Topics in Geometric Flows and Minimal Surfaces (St. Mary's College)

    Organizers: Ailana Fraser (University of British Columbia), Lan-Hsuan Huang (University of Connecticut), Catherine Searle (Wichita State University), Lu Wang (Yale University)
    Soap bubble: equilibrium solution of the rescaled mean curvature flow and constant curvature surface.

    This graduate summer school will introduce students to two important and inter-related fields of differential geometry: geometric flows and minimal surfaces.

    Geometric flows have had far reaching influences on numerous branches of mathematics and other scientific disciplines. An outstanding example is the completion of Hamilton’s Ricci flow program by Perelman, leading to the resolution of the Poincare conjecture and Thurston’s geometrization conjecture for 3-manifolds. In this part of the summer school, students will be guided through basic topics and ideas in the study of geometric flows.

    Since Penrose used variations of volume to formulate and study black holes in general relativity (in his Nobel prize-winning work), the intriguing connections between minimal surfaces and general relativity have been a strong driving force for the modern developments of both research areas. This part of the summer school will introduce students to the basic theory of minimal submanifolds and its applications in Riemannian geometry and general relativity.

    The curriculum of this program will be accessible and will have a broad appeal to graduate students from a variety of mathematical areas, introducing some of the latest developments in each area and the remaining open problems therein, while simultaneously emphasizing their synergy.

    Updated on Nov 03, 2022 11:58 AM PDT
  21. Summer Graduate School Machine Learning (UC San Diego)

    Organizers: Ery Arias-Castro (University of California, San Diego), Mikhail Belkin (University of California, San Diego), Yusu Wang (Univ. California, San Diego), Lily Weng (University of California, San Diego)

    The overarching goal of this summer school is to expose the students both to modern forms of unsupervised learning — in the form of geometrical and topological data analysis — and to supervised learning — in the form of (deep) neural networks applied to regression/classification problems. The organizers have opted for a lighter exposure to a broader range of topics. Using the metaphor of a meal, we are offering 2 + 2 samplers — geometry and topology for data analysis + theoretical and practical deep learning — rather than 1 + 1 main dishes. The main goal, thus, is to inspire the students to learn more about one or several of the topics covered in the school.

    The expected learning outcomes for students attending the school are the following:

    1. An introduction to how concepts and tools from geometry and topology can be leveraged to perform data analysis in situations where the data are not labeled.

    2. An introduction to recent and ongoing theoretical and methodological/practical developments in the use of neural networks for data analysis (deep learning).

    Updated on Nov 16, 2022 09:26 AM PST
  22. Summer Graduate School Introduction to Derived Algebraic Geometry (UC Berkeley)

    Organizers: Benjamin Antieau (Northwestern University), Dmytro Arinkin (University of Wisconsin-Madison)
    Schur quartic x 4−xy3 = z 4−zu3 and several of the 64 lines that it contains

    Derived algebraic geometry is an ‘update’ of algebraic geometry using ‘derived’ (roughly speaking, homological) techniques. This requires recasting the very foundations of the field: rings have to be replaced by differential graded algebras (or other forms of derived rings), categories by higher categories, and so on. The result is a powerful set of new tools, useful both within algebraic geometry and in related areas. The school serves as an introduction to these techniques, focusing on their applications.

    The school is built around two related courses on geometric (‘derived spaces’) and categorical (‘derived categories’) aspects of the theory. Our goal is to explain the key ideas and concepts, while trying to keep technicalities to a minimum.

    Updated on Nov 03, 2022 11:58 AM PDT
  23. Summer Graduate School Concentration Inequalities and Localization Techniques in High Dimensional Probability and Geometry (SLMath)

    Organizers: Max Fathi (Université Paris Cité), Dan Mikulincer (Massachusetts Institute of Technology)

    The goal of the summer school is for the students to first become familiar with the concept of concentration of measure in different settings (Euclidean, Riemannian and discrete), and the main open problems surrounding it. The students will later become familiar with the proof techniques that involve the different types of localization and obtain expertise on the ways to apply the localization techniques. After attending the graduate school, the students are expected to have the necessary background that would give them a chance to both conduct research around open problems in concentration of measure, find new applications to existing localization techniques and perhaps also develop new localization techniques.

    Updated on Nov 29, 2022 02:32 PM PST
  24. Summer Graduate School Mathematics of Big Data: Sketching and (Multi-) Linear Algebra (IBM Almaden)

    Organizers: Kenneth Clarkson (IBM Research Division), Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University), Tamara Kolda (MathSci.ai), Shashanka Ubaru (IBM Thomas J. Watson Research Center)

    This summer school will introduce graduate students to sketching-based approaches to computational linear and multi-linear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.

    Updated on Nov 03, 2022 11:59 AM PDT
  25. Program Mathematical Problems in Fluid Dynamics, part 2


    Fluid dynamics is one of the classical areas of partial differential equations, and has been the subject of extensive research over hundreds of years. It is perhaps one of the most challenging and exciting fields of scientific pursuit simply because of the complexity of the subject and the endless breadth of applications.

    The focus of the program is on incompressible fluids, where water is a primary example. The fundamental equations in this area are the well-known Euler equations for inviscid fluids, and the Navier-Stokes equations for the viscous fluids. Relating the two is the problem of the zero viscosity limit, and its connection to the phenomena of turbulence. Water waves, or more generally interface problems in fluids, represent another target area for the program. Both theoretical and numerical aspects will be considered.

    Updated on Oct 04, 2022 04:03 PM PDT
  26. Summer Graduate School Foundations and Frontiers of Probabilistic Proofs (Zürich, Switzerland)

    Organizers: Alessandro Chiesa (École Polytechnique Fédérale de Lausanne (EPFL))
    Proofs main logo
    Several executions of a 3-dimensional sumcheck protocol with a random order of directions (thanks to Dev Ojha for creating the diagram)

    Proofs are at the foundations of mathematics. Viewed through the lens of theoretical computer science, verifying the correctness of a mathematical proof is a fundamental computational task. Indeed, the P versus NP problem, which deals precisely with the complexity of proof verification, is one of the most important open problems in all of mathematics.

    The complexity-theoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit local-to-global structure that allows verifying a proof by reading only a minuscule portion of it. As another example, interactive proofs allow for verification via a conversation between a prover and a verifier, instead of the traditional static sequence of logical statements. The study of such proof systems has drawn upon deep mathematical tools to derive numerous applications to the theory of computation and beyond.

    In recent years, such probabilistic proofs received much attention due to a new motivation, delegation of computation, which is the emphasis of this summer school. This paradigm admits ultra-fast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recently-deployed technology, for example, as part of cryptographic constructions known as succinct non-interactive arguments of knowledge (SNARKs).

    This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.

    Updated on Nov 17, 2022 08:59 AM PST
  27. Program Mathematics and Computer Science of Market and Mechanism Design

    Organizers: Michal Feldman (Tel-Aviv University), Nicole Immorlica (Microsoft Research), LEAD Scott Kominers (Harvard Business School), Shengwu Li (Harvard University), Paul Milgrom (Stanford University), Alvin Roth (Stanford University), Tim Roughgarden (Stanford University), Eva Tardos (Cornell University)

    In recent years, economists and computer scientists have collaborated with mathematicians, operations research experts, and practitioners to improve the design and operations of real-world marketplaces. Such work relies on robust feedback between theory and practice, inspiring new mathematics closely linked – and directly applicable – to market and mechanism design questions. This cross-disciplinary program seeks to expand the domains in which existing market design solutions can be applied; address foundational questions regarding our ways of developing and evaluating mechanisms; and build useful analytic frameworks for applying theory to practical marketplace design.

    Updated on Nov 11, 2022 01:37 PM PST
  28. Program Algorithms, Fairness, and Equity

    Organizers: Vincent Conitzer (Carnegie Mellon University), Moon Duchin (Tufts University), Bettina Klaus (University of Lausanne), Jonathan Mattingly (Duke University), LEAD Wesley Pegden (Carnegie Mellon University)
    A graphical representation of a Markov Chain fairness analysis of a political districting in North Carolina from Chin, Herschlag, Mattingly

    This program aims to bring together researchers working at the interface of fairness and computation. This interface has been the site of intensive research effort in mechanism design, in research on partitioning problems related to political districting problems, and in research on ways to address issues of fairness and equity in the context of machine learning algorithms.

    These areas each approach the relationship between mathematics and fairness from a distinct perspective. In mechanism design, algorithms are a tool to achieve outcomes with mathematical guarantees of various notions of fairness. In machine learning, we perceive failures of fairness as an undesirable side effect of learning approaches, and seek mathematical approaches to understand and mitigate these failures. And in partitioning problems like political districting, we often seek mathematical tools to evaluate the fairness of human decisions.

    This program will explore progress in these areas while also providing a venue for overlapping perspectives. The topics workshop “Randomization, neutrality, and fairness” will explore the common role randomness and probability has played in these lines of work.

    Updated on Nov 11, 2022 01:41 PM PST
  29. Program Complementary Program 2023-24

    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 Dec 07, 2022 03:59 PM PST
  30. Workshop Connections Workshop: Algorithms, Fairness, and Equity

    Organizers: Vincent Conitzer (Carnegie Mellon University), LEAD Rachel Cummings (Columbia University), Ana-Andreea Stoica (University of California, Berkeley)

    The Connections Workshop will welcome participants of all genders and identities, with the scope of fostering a sense of community, amplifying voices of those who identify as women, and providing avenues to allies to be helpful. The workshop particularly aims to increase visibility among junior women in fields adjacent to the topics of the general program, including but not limited to game-theoretic fairness, mechanism design, partition, networks, redistricting, and fairness in machine learning. This two-day workshop will include keynote speakers, lightning talks from participants, panel discussions on career advancement, breakout sessions by research areas, opportunities for networking, and other mentoring activities.

    Updated on Jan 03, 2023 03:41 PM PST
  31. Program Commutative Algebra

    Organizers: Aldo Conca (Università di Genova), Steven 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)
    9 points theorem
    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 May 24, 2022 10:29 AM PDT
  32. Program Noncommutative Algebraic Geometry

    Organizers: Wendy Lowen (Universiteit Antwerp), Alexander Perry (University of Michigan), LEAD Alexander Polishchuk (University of Oregon), Susan Sierra (University of Edinburgh), Spela Spenko (Université Libre de Bruxelles), Michel Van den Bergh (Hasselt University)
    Optical illusion staircase

    Derived categories of coherent sheaves on algebraic varieties were originally conceived as technical tools for studying cohomology, but have since become central objects in fields ranging from algebraic geometry to mathematical physics, symplectic geometry, and representation theory. Noncommutative algebraic geometry is based on the idea that any category sufficiently similar to the derived category of a variety should be regarded as (the derived category of) a “noncommutative algebraic variety”; examples include semiorthogonal components of derived categories, categories of matrix factorizations, and derived categories of noncommutative dg-algebras. This perspective has led to progress on old problems, as well as surprising connections between seemingly unrelated areas. In recent years there have been great advances in this domain, including new tools for constructing semiorthogonal decompositions and derived equivalences, progress on conjectures relating birational geometry and singularities to derived categories, constructions of moduli spaces from noncommutative varieties, and instances of homological mirror symmetry for noncommutative varieties. The goal of this program is to explore and expand upon these developments. 

    Updated on May 19, 2022 01:51 PM PDT
  33. Workshop Connections Workshop: Commutative Algebra

    Organizers: Christine Berkesch (University of Minnesota, Twin Cities), Louiza Fouli (New Mexico State University), Maria Evelina Rossi (Università di Genova), LEAD Alexandra Seceleanu (University of Nebraska)
    Emmy Noether (1882-1935), a prominent founder of commutative ring theory

    This two-day workshop will feature the work of mathematicians in commutative algebra who identify as women or another marginalized gender. The talks will be appropriate for graduate students, post-docs, and researchers in areas related to the program. This meeting aims to support young researchers. The format will include plenary talks, poster sessions, panel discussions, as well as the opportunity for informal discussions and connections.  The workshop is open to all mathematicians, and members of historically excluded groups and identities are especially encouraged to attend.

    Updated on Nov 04, 2022 04:05 PM PDT
  34. Workshop Introductory Workshop: Commutative Algebra

    Organizers: Srikanth Iyengar (University of Utah), Claudia Miller (Syracuse University), Claudia Polini (University of Notre Dame), LEAD Anurag Singh (University of Utah)
    Msri 1053 image
    Fractal behavior of local cohomology. For details, see arXiv:2210.03656 by Gao and Raicu

    The Introductory Workshop will feature lecture series devoted to some recent breakthrough results in commutative algebra, and to new developments in core areas of the field.  It will also highlight links to other areas such as arithmetic geometry, representation theory, noncommutative geometry, and singularity theory.

    Updated on Oct 31, 2022 04:02 PM PDT
  35. Workshop Artin groups and arrangements: topology, geometry, and combinatorics

    Organizers: Christin Bibby (Louisiana State University), Ruth Charney (Brandeis University), Giovanni Paolini (California Institute of Technology), Mario Salvetti (Università di Pisa)
    Affine arrangement
    The affine line arrangement of type C with different lattices and toric arrangements arising from it.

    This workshop brings together experts from different areas to discuss and foster collaboration on several topics of current interest related to Artin groups such as the K(π, 1) conjecture, hyperplane arrangements and abelian arrangements, combinatorial structures associated with dual Coxeter systems, and complexes of nonpositive curvature.

    Updated on Dec 05, 2022 10:47 AM PST
  36. Workshop Recent Developments in Noncommutative Algebraic Geometry

    Organizers: Arend Bayer (University of Edinburgh), Graham Leuschke (Syracuse University), Alexander Polishchuk (University of Oregon), Susan Sierra (University of Edinburgh), Yan Soibelman (Kansas State University), Spela Spenko (Université Libre de Bruxelles), Gregory Stevenson (Aarhus University)
    Optical illusion staircase

    This workshop will give an overview of recent developments in non-commutative algebraic geometry, including NC projective AG, NC resolutions, semiorthogonal decompositions, enhancements of derived categories, and connections to homological mirror symmetry, to enumerative AG, to moduli spaces and to birational geometry. It will in particular focus on speakers who have built new bridges between these topics.

    Updated on Nov 30, 2022 09:03 AM PST
  37. Workshop Recent Developments in Commutative Algebra

    Organizers: Daniel Erman (University of Wisconsin-Madison), Linquan Ma (Purdue University), LEAD Karl Schwede (University of Utah), Karen Smith (University of Michigan), Andrew Snowden (University of Michigan), Irena Swanson (Purdue University)

    Many long-standing conjectures in commutative algebra have been solved in recent years, often through the introduction of new methods that are quickly becoming central to the field.  This workshop will bring together a wide array of researchers in commutative algebra and related fields, with the goal of forging new connections among topics, and with a particular emphasis on transformative new methods.

    Created on Jul 27, 2022 02:01 PM PDT
  38. Workshop Advances in Lie Theory, Representation Theory and Combinatorics: Inspired by the work of Georgia M. Benkart

    Organizers: Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), Ellen Kirkman (Wake Forest University), Gail Letzter, Daniel Nakano (University of Georgia), Arun Ram (University of Melbourne)

    This workshop will have a view to the future of a broad spectrum of topics including

    • structure and classification of finite dimensional Lie algebras and superalgebras in characteristic p
    • structure of infinite dimensional Lie algebras and their representations
    • deformation theory of algebras, double constructions and elemental Lie algebras
    • diagram algebras and combinatorial representation theory
    • algebraic combinatorics of groups of Lie type:characters, Schur-Weyl duality, Bratteli diagrams, and McKay correspondences
    • quantum groups and crystal bases, particularly for superalgebras and affine algebras
    • examples of fusion categories arising from representations of Drinfeld doubles and other algebras
    • cohomology for finite tensor categories with applications to its underlying geometry

    This meeting will feature principal contributors in these areas in a celebration of the work of Georgia Benkart. With the same focus and tenacity that Georgia always had, we will strive to provide a conference full of beautiful mathematics, incredible inspiration, and the warmth of Georgia’s welcoming personality to our field and our community.

    Updated on Dec 08, 2022 08:40 AM PST
  39. Program New Frontiers in Curvature: Flows, General Relativity, Minimal Submanifolds, and Symmetry

    Organizers: LEAD Ailana Fraser (University of British Columbia), Lan-Hsuan Huang (University of Connecticut), Richard Schoen (University of California, Irvine), LEAD Catherine Searle (Wichita State University), Lu Wang (Yale University), Guofang Wei (University of California, Santa Barbara)
    Gpr 2024 25 fall image vs2 fraser.2020.03.01
    Soap bubble: equilibrium solution of the mean curvature flow and constant curvature surface.

    Geometry, PDE, and Relativity are subjects that have shown intriguing interactions in the past several decades, while simultaneously diverging, each with an ever growing number of branches. Recently, several major breakthroughs have been made in each of these fields using techniques and ideas from the others. 

    This program is aimed at connecting various branches of Geometry, PDE, and Relativity and at enhancing collaborations across these disciplines and will include four main topics: Geometric Flows, Geometric problems in Mathematical Relativity, Global Riemannian Geometry, and Minimal Submanifolds. Specifically the program focuses on a central goal, which is to advance our knowledge toward Riemannian (sub)manifolds under geometric conditions, such as curvature lower bounds, by developing techniques in, for example, geometric flows and minimal submanifolds and further fostering new connections.

    Updated on Nov 17, 2022 10:10 AM PST
  40. Program Special Geometric Structures and Analysis

    Organizers: Eleonora Di Nezza (Institut de Mathématiques de Jussieu), LEAD Mark Haskins (Duke University), Tristan Riviere (ETH Zurich), Song Sun (University of California, Berkeley), Xuwen Zhu (Northeastern University)
    “Plateau’s Memory ” (by A. van der Net): A soap film with singularities

    This program sits at the intersection between differential geometry and analysis but also connects to several other adjacent mathematical fields and to theoretical physics. Differential geometry aims to answer questions about very regular geometric objects (smooth Riemannian manifolds) using the tools of differential calculus. A fundamental object is the curvature tensor of a Riemannian metric: an algebraically complicated object that involves 2nd partial derivatives of the metric. Many questions in differential geometry can therefore be translated into questions about the existence or properties of the solutions of systems of (often) nonlinear partial differential equations (PDEs). The PDE systems that arise in geometry have historically stimulated the development of powerful new analytic methods. In most cases the nonlinearity of these systems makes ‘closed form’ expressions for a solution impossible: instead more abstract methods must be employed.

    Updated on Nov 10, 2022 04:20 PM PST
  41. Program Probability and Statistics of Discrete Structures

    Organizers: Louigi Addario-Berry (McGill University), Christina Goldschmidt (University of Oxford), Po-Ling Loh (University of Cambridge), Gabor Lugosi (Universitat Pompeu Fabra), Dana Randall (Georgia Institute of Technology), LEAD Remco van der Hofstad (Technische Universiteit Eindhoven)
    Psds image small
    The minimum spanning tree of 100,000 uniformly random points. Colors encode graph distance from the root, which is red. Black points are those whose removal would disconnect at least 5% of the points from the rest.

    Random graphs and related random discrete structures lie at the forefront of applied probability and statistics, and are core topics across a wide range of scientific disciplines where mathematical ideas are used to model and understand real-world networks. At the same time, random graphs pose challenging mathematical and algorithmic problems that have attracted attention from probabilists and combinatorialists since at least 1960, following the pioneering work of Erdos and Renyi.

    Around the turn of the millennium, as very large data sets became available, several applied disciplines started to realize that many real-world networks, even though they are from various origins, share fascinating features. In particular, many such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scale-free, in the sense that the number of connections made by their elements is extremely heterogeneous. This program is devoted to the study of the probabilistic and statistical properties of such networks. Central tools include graphon theory for dense graphs, local weak convergence for sparse graphs, and scaling limits for the critical behavior of graphs or stochastic processes on them. The program is aimed at pure and applied mathematicians interested in network problems.

    Updated on Nov 21, 2022 03:40 PM PST

Past Scientific Events

  1. Workshop Introductory 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

    This will be a hybrid workshop with both in-person and virtual participation.

    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. This workshop is held in honor of mathematician Bernadette Perrin-Riou.

    Updated on Jan 27, 2023 02:49 PM PST
  2. Workshop Connections 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)
    Portrait pure
    David Lowry-Duda. Modular form of weight 32 and level 3. For details, see http://davidlowryduda.com/trace-form/

    This will be a hybrid workshop with both in-person and virtual participation.

    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. This workshop is held in honor of mathematician Bernadette Perrin-Riou.

    Updated on Jan 27, 2023 02:45 PM PST
  3. Seminar Journal Club

    Updated on Oct 13, 2022 12:54 PM PDT
  4. Seminar Q&A Session

    Updated on Dec 09, 2022 11:18 AM PST
  5. Seminar Journal Club

    Updated on Oct 13, 2022 12:53 PM PDT
  6. Seminar What Is Seminar

    Updated on Sep 27, 2022 02:44 PM PDT
  7. Seminar Journal Club

    Updated on Oct 13, 2022 12:51 PM PDT
There are more then 25 past events. Please go to Past Events to see all past events.