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1. African Diaspora Joint Mathematics2021 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 21 to July 2, 2021.

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 Jun 11, 2021 12:48 PM PDT
2. Summer Graduate SchoolMathematics of Big Data: Sketching and (Multi-) Linear Algebra (Virtual School)

Organizers: LEAD Kenneth Clarkson (IBM Research Division), Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University), Tamara Kolda (Sandia National Laboratories), 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 Mar 15, 2021 03:16 PM PDT
3. Summer Graduate SchoolGauge Theory in Geometry and Topology (Virtual School)

Organizers: Lynn Heller (Universität Hannover), Francesco Lin (Columbia University), LEAD Laura Starkston (University of California, Davis), Boyu Zhang (Princeton University)
Image by Nick Schmitt

Figure 1. A rotationally symmetric solution to the self-duality equations on an open and dense subset of the torus. Singularities appear where the surface intersects the ideal boundary at infinity of the hyperbolic 3-space visualized by the wireframe.

Gauge theory is a geometric language used to formulate many fundamental physical phenomena, which has also had profound impact on our understanding of topology. The main idea is to study the space of solutions to partial differential equations admitting a very large group of local symmetries. Starting in the late 1970s, mathematicians began to unravel surprising connections between gauge theory and many aspects of geometric analysis, algebraic geometry and low-dimensional topology. This influence of gauge theory in geometry and topology is pervasive nowadays, and new developments continue to emerge.

The goal of the summer school is to introduce students to the foundational aspects of gauge theory, and explore their relations to geometric analysis and low-dimensional topology. By the end of the two-week program, the students will understand the relevant analytic and geometric aspects of several partial differential equations of current interest (including the Yang-Mills ASD equations, the Seiberg-Witten equations, and the Hitchin equations) and some of their most impactful applications to problems in geometry and topology.

Updated on Jun 10, 2021 09:28 AM PDT
4. Summer Graduate SchoolRandom Conformal Geometry (Virtual School)

Organizers: Mario Bonk (University of California, Los Angeles), Steffen Rohde (University of Washington), LEAD Fredrik Viklund (Royal Institute of Technology)
a random quasiconformal map obtained from Beltrami equation by randomly assigning the values of +-1/2 for the Beltrami coefficient on small squares subdividing the unit square

This Summer Graduate School will cover basic tools that are instrumental in Random Conformal Geometry (the investigation of analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics) and are at the foundation of the subsequent semester-long program  "The Analysis and Geometry of Random Spaces".  Specific topics are Conformal Field Theory, Brownian Loops and related processes, Quasiconformal Maps, as well as Loewner Energy and Teichmüller Theory.

Updated on Mar 19, 2021 03:03 PM PDT
5. Summer Graduate SchoolFoundations and Frontiers of Probabilistic Proofs (Virtual School)

Organizers: Alessandro Chiesa (University of California, Berkeley), Tom Gur (University of Warwick)
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 Apr 19, 2021 06:23 PM PDT
6. ProgramOffsite Postdoctoral Fellowship 2021/22

Created on Feb 05, 2021 03:15 PM PST
7. SeminarUniversality and Integrability in Random Matrix Theory and Interacting Particle Systems - Virtual Participant

Updated on Apr 05, 2021 09:24 AM PDT
8. 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 Apr 20, 2020 11:12 AM PDT
9. 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
10. WorkshopConnections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1

Organizers: Gerard Ben Arous (New York University, Courant Institute), Ioana Dumitriu (University of California, San Diego), Alice Guionnet (École Normale Supérieure de Lyon), Alisa Knizel (The University of Chicago), Sylvia Serfaty (New York University, Courant Institute), Horng-Tzer Yau (Harvard University)

This will be a hybrid workshop with in-person participation by invitation only. Online participation will be open to all who register. This workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

Updated on Jun 16, 2021 01:13 PM PDT
11. WorkshopConnections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 2

Organizers: Gerard Ben Arous (New York University, Courant Institute), Ioana Dumitriu (University of California, San Diego), Alice Guionnet (École Normale Supérieure de Lyon), Alisa Knizel (The University of Chicago), Sylvia Serfaty (New York University, Courant Institute), Horng-Tzer Yau (Harvard University)
An illustration of the TASEP interface growth by Leonid Petrov and Hao Yu Li.

We anticipate that this will be an in-person workshop (subject to change based on COVID rules). Online participation will also be possible. The speakers will be a subset of the original speakers for the Connections and Introductory Workshops.

This workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

In addition, this workshop will also explore connections with other branches of mathematics and applications to sciences and engineering. The workshop will feature presentations by both leading researchers and promising newcomers. There will be some special activities originally planned for the Connections Workshop: We will have a panel discussion of topics relevant to junior researchers, women, and minorities; a poster session for students and recent PhDs; and other social events.

This workshop is open to and welcomes all mathematicians.

Updated on Jun 16, 2021 01:13 PM PDT
12. WorkshopIntegrable 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 Péché (Université de Paris VII (Denis Diderot))
Image by Alexei Borodin.

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 Jul 31, 2019 03:22 PM PDT
13. 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))

The 2020 Blackwell-Tapia Conference has been rescheduled to 2021.  The Prize Winner is Tatiana Toro, Professor of Mathematics, University of Washington.

Description: Held every other year, the conference and prize honor David Blackwell, the first African-American member of the National Academy of Science, and Richard Tapia, winner of the National Medal of Science in 2010, two seminal figures who inspired a generation of African-American, Native American, and Latino/Latina students to pursue careers in mathematics. The Blackwell-Tapia Prize recognizes a mathematician who has contributed significantly to research in his or her area of expertise, and who has served as a role model for mathematical scientists and students from underrepresented minority groups or has contributed in other significant ways to addressing the problem of under-representation of minorities in math.

Updated on Jun 02, 2021 11:33 AM PDT
14. SeminarThe Analysis and Geometry of Random Spaces - Virtual Participant

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

Updated on Apr 07, 2021 10:49 AM PDT
16. 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
17. 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 Toulouse), 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
18. 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
19. 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 Mar 24, 2021 10:16 AM PDT
20. 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 Mar 17, 2021 09:28 AM PDT
21. 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
22. WorkshopHot Topics: Foundations of Stable, Generalizable and Transferable Statistical Learning

Organizers: LEAD Peter Buhlmann (ETH Zurich), John Duchi (Stanford University), Elizabeth Tipton (Northwestern University), Bin Yu (University of California, Berkeley)

Updated on Jun 14, 2021 10:30 AM PDT
23. WorkshopHot Topics: Regularity Theory for Minimal Surfaces and Mean Curvature Flow

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

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 Jun 14, 2021 10:18 AM PDT
24. 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 Jan 05, 2021 03:32 PM PST

Organizers: Mikhail Lyubich (State University of New York, Stony Brook), LEAD Jasmin Raissy (Institut de Mathématiques de Toulouse), LEAD Roland Roeder (Indiana University--Purdue University), Dierk Schleicher (Université d'Aix-Marseille (AMU)), Mitsuhiro Shishikura (Kyoto University)
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
26. 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.

Created on Apr 29, 2021 10:45 AM PDT
27. 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
28. 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
29. 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
30. 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
31. 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 mini-courses aimed at graduate students and other researchers who are new to the field, as well as a sequence of research talks. There will also be a "fireside chat" 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 Mar 05, 2021 02:47 PM PST
32. 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)

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
33. 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
34. 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
35. 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
36. 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 (Université Paris-Sud), 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
37. 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
38. 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