# Mathematical Sciences Research Institute

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1. # Connections 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
2. # Connections 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
3. # Integrable structures in random matrix theory and beyond

Organizers: LEAD Jinho Baik (University of Michigan), Alexei Borodin (Massachusetts Institute of Technology), Tamara Grava (University of Bristol; International School for Advanced Studies (SISSA/ISAS)), Alexander Its (Indiana University--Purdue University), Sandrine 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
4. # Blackwell 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
5. # Connections 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
6. # Introductory 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
7. # 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 (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
8. # 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 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
9. # Hot 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
10. # Hot 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
11. # 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 05, 2021 03:32 PM PST
12. # Adventurous Berkeley Complex Dynamics

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
13. # Connections 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
14. # 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
15. # 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 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
16. # 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)

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
17. # 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
18. # 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
19. # 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
20. # 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