# Mathematical Sciences Research Institute

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1. # [HYBRID WORKSHOP] Connections 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 (Université Paris-Saclay), Sarah Koch (University of Michigan)

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 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 Dec 07, 2021 08:45 AM PST
2. # [HYBRID WORKSHOP] Introductory 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 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 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 Jan 26, 2022 12:19 PM PST
3. # [Virtual] Hot 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 Jan 26, 2022 12:02 PM PST
4. # [Hybrid Workshop] Critical Issues in Mathematics Education 2022: Initiating, Sustaining, and Researching Mathematics Department Transformation of Introductory Courses for STEM Majors, Part 2

Organizers: Naneh Apkarian (Arizona State University), David Bressoud (Macalester College), Pamela Burdman (Just Equations), Jamylle Carter (Diablo Valley college), Ted Coe (Northwest Evaluation Association), Courtney Ginsberg (Math for America), Estrella Johnson (Virginia Polytechnic Institute and State University), W Gary Martin (Auburn University), Michael O'Sullivan (San Diego State University), William Penuel (University of Colorado), LEAD Chris Rasmussen (San Diego State University), Daniel Reinholz (San Diego State University), Wendy Smith (University of Nebraska), David Webb (University of Colorado at Boulder)

The world is changing, along with perceptions. Many call for the improvement of mathematics teaching and learning, for both citizenry and STEM preparation. To achieve sustainable change, though, the focus needs to extend from individuals to systems. It is not enough to change one classroom or one course. Transformation requires change at all levels: in teaching, programmatic practices, and institutions. This workshop will bring together teachers and researchers from universities, community colleges, and K-12 schools to explore the reasons for and processes by which change in university mathematics departments is initiated, promoted, and sustained and lessons learned from change efforts in K-12. It will review what we know about change at all levels and reflect on stories of failure and success.

Updated on Jan 26, 2022 12:17 PM PST
5. # [Virtual] Hot 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 Jan 26, 2022 12:04 PM PST
6. # The 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 Jan 26, 2022 12:06 PM PST
7. # Adventurous 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
8. # Connections Workshop: Analytic and Geometric Aspects of Gauge Theory

Organizers: Lara Anderson (Virginia Polytechnic Institute and State 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
9. # Introductory 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
10. # Connections 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
11. # Introductory 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
12. # New 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
13. # Floer 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
14. # 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)
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
15. # 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

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
16. # Connections Workshop: Diophantine Geometry

Organizers: Jennifer Balakrishnan (Boston University), LEAD Yunqing Tang (Princeton University)

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 Dec 17, 2021 02:42 PM PST
17. # Introductory Workshop: Diophantine Geometry

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

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 Dec 20, 2021 09:18 AM PST
18. # 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 (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
19. # Degeneracy of algebraic points

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

Updated on Nov 02, 2021 01:30 PM PDT