
Program Holomorphic Differentials in Mathematics and Physics
Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at UrbanaChampaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anna Wienhard (RuprechtKarlsUniversität Heidelberg), Anton Zorich (Institut de Mathematiques de Jussieu)Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukayatype categories, links to quantum integrable systems, or the physically derived construction of socalled spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special  Hitchin or higher Teichmuller  components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).
It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our program will be of interest to those working in many different elds, including lowdimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).
Updated on Nov 13, 2019 01:37 PM PST 
Program Microlocal Analysis
Organizers: Pierre Albin (University of Illinois at UrbanaChampaign), Nalini Anantharaman (Université de Strasbourg), Kiril Datchev (Purdue University), Raluca Felea (Rochester Institute of Technology), Colin Guillarmou (Université de Paris XI (ParisSud)), LEAD Andras Vasy (Stanford University)Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This program will bring together researchers from various parts of the field to facilitate the transfer of ideas, and will also provide a comprehensive introduction to the field for postdocs and graduate students.
Updated on Apr 13, 2018 11:42 AM PDT 
Program Complementary Program 201920
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 Nov 27, 2018 12:28 PM PST 
Workshop Holomorphic Differentials in Mathematics and Physics
Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at UrbanaChampaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Laura Schaposnik (University of Illinois at Chicago), Gabriela WeitzeSchmithuesen (Universität des Saarlandes), Anton Zorich (Institut de Mathematiques de Jussieu)Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukayatype categories, links to quantum integrable systems, or the physically derived construction of socalled spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special  Hitchin or higher Teichmuller  components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).
It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our workshop will be of interest to those working in many different fields, including lowdimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).
Updated on May 14, 2018 02:00 PM PDT 
Seminar MLA  Regular Seminar (part 2): Elliptic families and pointclusters
Updated on Nov 19, 2019 03:15 PM PST

Seminar Learning seminar on stability conditions
Created on Sep 04, 2019 09:31 AM PDT 
Seminar MLA  Special Seminar:
Created on Nov 14, 2019 11:46 AM PST 
Seminar MLAGraduate Student Seminar
Created on Aug 26, 2019 02:41 PM PDT 
Seminar HDMPLunch Q&A session
Created on Oct 04, 2019 10:50 AM PDT 
Seminar MLA  Iterated structures on manifolds working group
Updated on Sep 25, 2019 11:18 AM PDT 
Seminar HDMP  Graduate Student Seminar
Created on Aug 27, 2019 02:13 PM PDT 
Seminar MLA  Weekly Seminar (Part 1)
Created on Aug 27, 2019 01:13 PM PDT 
Seminar MLA  Weekly Seminar (Part 2)
Created on Aug 27, 2019 01:18 PM PDT 
Seminar Learning seminar on stability conditions
Created on Sep 04, 2019 09:31 AM PDT 
Seminar MLAGraduate Student Seminar
Created on Aug 26, 2019 02:41 PM PDT 
Seminar Topics in Differential Geometry (Chancellor Course)
Updated on Sep 26, 2019 04:44 PM PDT 
Seminar HDMPLunch Q&A session
Created on Oct 04, 2019 10:50 AM PDT 
Seminar MLA  Iterated structures on manifolds working group
Updated on Sep 25, 2019 11:19 AM PDT 
Seminar HDMP  Graduate Student Seminar
Created on Aug 27, 2019 02:13 PM PDT 
Seminar HDMP  Weekly Seminar (Part 1)
Updated on Sep 26, 2019 01:33 PM PDT 
Seminar HDMPWeekly Seminar (Part 2)
Updated on Sep 26, 2019 01:51 PM PDT 
Seminar MLA  Weekly Seminar (Part 1)
Created on Aug 27, 2019 01:13 PM PDT 
Seminar MLA  Weekly Seminar (Part 2)
Created on Aug 27, 2019 01:18 PM PDT 
Seminar Topics in Differential Geometry (Chancellor Course)
Updated on Sep 26, 2019 04:44 PM PDT 
Seminar MLA  Regular Seminar (part 1):
Updated on Oct 18, 2019 12:23 PM PDT 
Seminar HDMP  Physics: a guide for the perplexed
Updated on Sep 04, 2019 03:19 PM PDT 
Seminar MLA  Regular Seminar (part 2):
Updated on Oct 18, 2019 12:27 PM PDT 
Seminar Spectral networks reading group
Created on Sep 05, 2019 03:05 PM PDT 
Workshop Symposium in Honor of Julia Robinson’s 100th Birthday
Organizers: Hélène Barcelo (MSRI  Mathematical Sciences Research Institute), Thomas Scanlon (University of California, Berkeley), Carol Wood (Wesleyan University)MSRI will host a Symposium on the occasion of Julia Robinson’s 100th birthday on Monday, December 9, 2019 at MSRI. Julia Robinson (19191985) was an internationally renowned logician of the twentieth century. She was a trailblazer in mathematics as well as in many other ways: she was the first woman president of the American Mathematical Society, and the first woman mathematician elected to membership in the National Academy of Sciences.
Participating speakers in this daylong celebration of her work and of current mathematics insprired by her research include: Martin Davis, Kirsten Eisentrager, Yuri Matiyasevich, and Lou van den Dries. Following the symposium, Lenore Blum will give a public lecture at UC Berkeley.
Updated on Nov 15, 2019 10:41 AM PST 
Seminar Learning seminar on stability conditions
Created on Sep 04, 2019 09:31 AM PDT 
Seminar MLAGraduate Student Seminar
Created on Aug 26, 2019 02:41 PM PDT 
Seminar Topics in Differential Geometry (Chancellor Course)
Created on Nov 15, 2019 10:40 AM PST 
Seminar HDMPLunch Q&A session
Created on Oct 04, 2019 10:50 AM PDT 
Seminar MLA  Iterated structures on manifolds working group
Updated on Sep 25, 2019 11:19 AM PDT 
Seminar HDMP  Graduate Student Seminar
Created on Aug 27, 2019 02:13 PM PDT 
Seminar HDMP  Weekly Seminar (Part 1)
Updated on Sep 26, 2019 01:34 PM PDT 
Seminar HDMPWeekly Seminar (Part 2)
Updated on Sep 26, 2019 01:52 PM PDT 
Seminar MLA  Weekly Seminar (Part 1)
Created on Aug 27, 2019 01:13 PM PDT 
Seminar MLA  Weekly Seminar (Part 2)
Created on Aug 27, 2019 01:18 PM PDT 
Seminar MLA  Regular Seminar (part 1):
Updated on Oct 18, 2019 12:24 PM PDT 
Seminar HDMP  Physics: a guide for the perplexed
Updated on Sep 04, 2019 03:19 PM PDT 
Seminar MLA  Regular Seminar (part 2):
Updated on Oct 18, 2019 12:28 PM PDT 
Program Quantum Symmetries
Organizers: Vaughan Jones (Vanderbilt University), LEAD Scott Morrison (Australian National University), Victor Ostrik (University of Oregon), Emily Peters (Loyola University), Eric Rowell (Texas A & M University), LEAD Noah Snyder (Indiana University), Chelsea Walton (University of Illinois at UrbanaChampaign)Symmetry, as formalized by group theory, is ubiquitous across mathematics and science. Classical examples include point groups in crystallography, Noether's theorem relating differentiable symmetries and conserved quantities, and the classification of fundamental particles according to irreducible representations of the Poincaré group and the internal symmetry groups of the standard model. However, in some quantum settings, the notion of a group is no longer enough to capture all symmetries. Important motivating examples include Galoislike symmetries of von Neumann algebras, anyonic particles in condensed matter physics, and deformations of universal enveloping algebras. The language of tensor categories provides a unified framework to discuss these notions of quantum symmetry.Updated on Mar 22, 2018 11:21 AM PDT 
Program Higher Categories and Categorification
Organizers: David Ayala (Montana State University), Clark Barwick (University of Edinburgh), David Nadler (University of California, Berkeley), LEAD Emily Riehl (Johns Hopkins University), Marcy Robertson (University of Melbourne), Peter Teichner (MaxPlanckInstitut für Mathematik), Dominic Verity (Macquarie University)Though many of the ideas in higher category theory find their origins in homotopy theory — for instance as expressed by Grothendieck’s “homotopy hypothesis” — the subject today interacts with a broad spectrum of areas of mathematical research. Unforeseen descent, or localtoglobal formulas, for familiar objects can be articulated in terms of higher invertible morphisms. Compatible associative deformations of a sequence of maps of spaces, or derived schemes, can putatively be represented by higher categories, as Koszul duality for E_nalgebras suggests. Higher categories offer unforeseen characterizing universal properties for familiar constructions such as Ktheory. Manifold theory is natively connected to higher category theory and adjunction data, a connection that is most famously articulated by the recently proven Cobordism Hypothesis.
In parallel, the idea of "categorification'' is playing an increasing role in algebraic geometry, representation theory, mathematical physics, and manifold theory, and higher categorical structures also appear in the very foundations of mathematics in the form of univalent foundations and homotopy type theory. A central mission of this semester will be to mitigate the exorbitantly high "cost of admission'' for mathematicians in other areas of research who aim to apply higher categorical technology and to create opportunities for potent collaborations between mathematicians from these different fields and experts from within higher category theory.Updated on Oct 05, 2018 12:21 PM PDT 
Workshop Connections for Women: Quantum Symmetries
Organizers: Emily Peters (Loyola University), LEAD Chelsea Walton (University of Illinois at UrbanaChampaign)This workshop will feature several talks by experts, along with numerous 5minute presentations by junior mathematicians, on topics related to Quantum Symmetry. Such topics will include tensor categories, subfactors, Hopf algebras, topological quantum field theory and more. There will also be a panel discussion 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 01, 2019 04:19 PM PDT 
Workshop Introductory Workshop: Quantum Symmetries
Organizers: Vaughan Jones (Vanderbilt University), Victor Ostrik (University of Oregon), Emily Peters (Loyola University), LEAD Noah Snyder (Indiana University)This workshop will consist of introductory minicourses on key topics in Quantum Symmetry: fusion categories, modular tensor categories, Hopf algebras, subfactors and planar algebras, topological field theories, conformal nets, and topological phases of matter. These minicourses will be introductory and are aimed at giving semester participants exposure to the main ideas of subfields other than their own.
Updated on Apr 09, 2018 02:20 PM PDT 
Workshop Connections for Women: Higher Categories and Categorification
Organizers: Emily Riehl (Johns Hopkins University), LEAD Marcy Robertson (University of Melbourne)This twoday workshop will survey notable developments in the foundations and applications of higher category theory. It will consist of two minicourses given by emerging female leaders in the subject: Claudia Scheimbauer and Nathalie Wahl. This will be paired with a problem sessions lead by selected "TA's", themselves experts in higher structures. Each lecture series will be tailored to a diverse audience, accessible to graduate students and nonexpert researchers with some background in homological algebra.
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 01, 2019 04:20 PM PDT 
Workshop Introductory Workshop: Higher Categories and Categorification
Organizers: LEAD David Ayala (Montana State University), Emily Riehl (Johns Hopkins University), Christopher SchommerPries (University of Notre Dame), Peter Teichner (MaxPlanckInstitut für Mathematik)This workshop will survey notable developments and applications of higher category theory; it will be a venue for endusers to share their vision of how to apply the theory, as well as developers to share technical advancements. It will consist of 6 series of 3 lectures, each given by instrumental endusers & developers of higher category theory, together with a few questionanswer sessions. Each lecture series will be tailored to a diverse audience, accessible to graduate students and nonexpert researchers with some background in homological also algebra. The content of these lecture series will concern the following topics.
 Ktheory: categorification, noncommutative motives, trace methods;
 TQFT: functorial field theories, factorization homology.
 Parametrized higher category theory: stratifications, equivariant homotopy theory, operads, deformation theory and Koszul duality.
 Synthetic higher category theory: modelindependent characterizations, cosmoi.
Updated on Sep 14, 2018 02:08 PM PDT 
Workshop Tensor categories and topological quantum field theories
Organizers: Scott Morrison (Australian National University), Eric Rowell (Texas A & M University), LEAD Claudia Scheimbauer (TU München), Christopher SchommerPries (University of Notre Dame)The workshop will concern the latest developments in the mathematical study of quantum field theories. The focus will be on the interplay among topics such as higher category theory, as illustrated by the cobordism hypothesis, conformal field theory, tensor categories describing the quantum symmetries, and the relation to topological phases of matter.
Updated on Jul 03, 2018 04:02 PM PDT 
Workshop (∞, n)categories, factorization homology, and algebraic Ktheory
Organizers: LEAD Clark Barwick (University of Edinburgh), David Gepner (University of Melbourne), David Nadler (University of California, Berkeley), Marcy Robertson (University of Melbourne)This workshop will focus on recent developments in factorization homology, parametrized homotopy theory, and algebraic Ktheory. These seemingly disparate topics are unified by a common methodology, which leverages universal properties and unforeseen descent by way of higher category theory. Furthermore, they enjoy powerful and complementary roles in application to the cyclotomic trace. This workshop will be a venue for experts in these areas to present new results, make substantive connections across fields, and suggest and contextualize outstanding questions and problems. It will consist of 9 speakers, each delivering a 1hour morning talk and a 1hour afternoon talk, in addition to a session reserved for drawing attention to an assortment of outstanding problems.
Updated on Sep 17, 2019 03:04 PM PDT 
Workshop Hot Topics: Optimal transport and applications to machine learning and statistics
Organizers: Luigi Ambrosio (Scuola Normale Superiore), Francis Bach (École Normale Supérieure), LEAD Katy Craig (University of California, Santa Barbara), CarolaBibiane Schönlieb (University of Cambridge), Stefano Soatto (University of California, Los Angeles)The goal of the workshop is to explore the many emerging connections between the theory of Optimal Transport and models and algorithms currently used in the Machine Learning community. In particular, the use of Wasserstein metrics and the relation between discrete models and their continuous counterparts will be presented and discussed.
Updated on Oct 24, 2019 02:42 PM PDT 
Summer Graduate School Combinatorial and DGAlgebra Techniques for Free Resolutions (Tianjin, China)
Organizers: Chengming Bai (Chern Institute of Mathematics), LEAD Dave Bayer (Columbia University), Claudia Miller (Syracuse University)The two topics, combinatorial theory of free resolutions and differential graded algebra techniques in homological algebra, each have a long and rich history in commutative algebra and its applications to algebraic geometry. Free resolutions are at the center of much of the study in the field and these two approaches give powerful tools for their study and their application to other problems. Neither of these topics is generally covered in graduate courses. Furthermore, recent developments have exhibited exciting interplay between the two subjects. The purpose of the school is to introduce the graduate students to these subjects and these new developments. The school will consist of two lectures each day and carefully planned problem sessions designed to reinforce the foundational material and to give them a chance to experiment with problems involving the interplay between the two subjects.
Updated on Jul 26, 2019 03:43 PM PDT 
MSRIUP MSRIUP 2020: Branched Covers of Curves
Organizers: Federico Ardila (San Francisco State University), LEAD Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI  Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), Edray Goins (Pomona College), Suzanne Weekes (Worcester Polytechnic Institute)The MSRIUP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
In 2020, MSRIUp will focus on Branched Covers of Curves. The research program will be led by Dr. Edray Goins, Professor of Mathematics at Pomona College.
Updated on Nov 18, 2019 04:20 PM PST 
Summer Research for Women in Mathematics 2020 Summer Research in Mathematics
MSRI's Summer Research in Mathematics program provides space, funding, and the opportunity for inperson collaboration to small groups of mathematicians, especially women and genderexpansive individuals, whose ongoing research may have been disproportionately affected by various obstacles including family obligations, professional isolation, or access to funding. Through this effort, MSRI aims to mitigate the obstacles faced by these small groups, improve the odds of research project completion, and deepen their research experience.
The ultimate goal of this program is to enhance the mathematical sciences as a whole by positively affecting the research and careers of all of its participants and assisting their efforts to maintain involvement in the research community.
The application period for the 2020 program is now open. To apply, please see this webpage.
Updated on Sep 26, 2019 09:50 AM PDT 
Summer Graduate School Algebraic Theory of Differential and Difference Equations, Model Theory and their Applications
Organizers: LEAD Alexey Ovchinnikov (City University of New York (CUNY)), Anand Pillay (University of Notre Dame), Gleb Pogudin (New York University, Courant Institute), Thomas Scanlon (University of California, Berkeley), Michael Wibmer (University of Notre Dame)The purpose of the summer school will be to introduce graduate students to effective methods in algebraic theories of differential and difference equations with emphasis on their modeltheoretic foundations and to demonstrate recent applications of these techniques to studying dynamic models arising in sciences. While these topics comprise a coherent and rich subject, they appear in graduate coursework in at best a piecemeal way, and then only as components of classes for other aims. With this Summer Graduate School, students will learn both the theoretical basis of differential and difference algebra and how to use these methods to solve practical problems. Beyond the lectures, the graduate students will meet daily in problem sessions and will participate in oneonone mentoring sessions with the lecturers and organizers.
Updated on Jul 26, 2019 03:42 PM PDT 
Summer Graduate School Geometric Flows (Athens, Greece)
Organizers: Nicholas Alikakos (National and Kapodistrian University of Athens (University of Athens)), Panagiota Daskalopoulos (Columbia University)[The image on this vase from Minoan Crete, dated on 15002000 BC, resembles an ancient solution to the Curve shortening flow  one of the most basic geometric flows. The vase is at Heraklion Archaeological Museum]
This summer graduate school is a collabroation between MSRI and the FORTHIACM Institute in Crete. The purpose of the school is to introduce graduate students to some of the most important geometric evolution equations.
This is an area of geometric analysis that lies at the interface of differential geometry and partial differential equations. The lectures will begin with an introduction to nonlinear diffusion equations and continue with classical results on the Ricci Flow, the Mean curvature flow and other fully nonlinear extrinsic flows such as the Gauss curvature flow. The lectures will also include geometric applications such as isoperimetric inequalities, topological applications such as the Poincaré onjecture, as well as recent important developments related to the study of singularities and ancient solutions.
Updated on Oct 11, 2019 12:39 PM PDT 
Summer Graduate School Séminaire de Mathématiques Supérieures 2020: Discrete Probability, Physics and Algorithms (Montréal, Canada)
Organizers: Gerard Ben Arous (New York University, Courant Institute), LEAD Alexander Fribergh (University of Montreal), Lea Popovic (Concordia University)Probability theory, statistics as well as mathematical physics have increasingly been used in computer science. The goal of this school is to provide a unique opportunity for graduate students and young researchers to developed multidisciplinary skills in a rapidly evolving area of mathematics.
The topics would include spin glasses, constraint satisfiability, randomized algorithms, MonteCarlo Markov chains and highdimensional statistics, sparse and random graphs, computational complexity, estimation and approximation algorithms. Those topics will fall into two main categories, on the one hand problems related to spin glasses and on the other hand random algorithms.
The part of the summer school dedicated to spin glasses will be split into three parts: an introductory course about traditional spin glasses followed by two more advanced courses where spin glasses meet computer science in addition to a talk on dynamics of spin glasses. The part of the summer school on random algorithms will consist of an introductory course on phase transitions in large random structures, followed by advanced courses on theoretical bounds for computational complexity in reconstruction and inference, and on understanding rare events in random graphs and models of statistical mechanics.
The two introductory courses on spin glasses and on random algorithms will be accompanied by three exercises sessions of one hour. A one hour exercises session will follow each of the three sessions of a course for both the introductory course on spin glasses and the introductory course on random algorithms. Exercises sessions will be led by an assistant, but will primarily focus on participation of the students.
Updated on Sep 18, 2019 03:30 PM PDT 
Summer Graduate School Random Graphs
Organizers: Louigi AddarioBerry (McGill University), Remco van der Hofstad (Technische Universiteit Eindhoven)The topic of random graphs is at the forefront of applied probability, and it is one of the central topics in multidisciplinary science where mathematical ideas are used to model and understand the real world. At the same time, random graphs pose challenging mathematical problems that have attracted the attention from probabilists and combinatorialists since the 1960, with the pioneering work of Erdös and Rényi. Around the turn of the millennium, very large data sets started to become available, and several applied disciplines started to realize that many realworld networks, even though they are from various different origins, share many fascinating features. In particular, many of such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scalefree, in the sense that there are enormous differences in the number of connections that their elements make. In particular, such networks are quite different from the classical random graph models, such as proposed by Erdös and Rényi.
Updated on Jul 26, 2019 03:40 PM PDT 
Summer Graduate School Algebraic Curves (Hainan, China)
Organizers: David Eisenbud (MSRI  Mathematical Sciences Research Institute), Joseph Harris (Harvard University)[Image: The simplest interesting case of linkage (liaison) of curves in projective 3space. We see two quadric surfaces, one of which is a cone, meeting in the union of a line (vertical in the illustration) and a twisted cubic (snaking up from the bottom left to the upper right, tangent to the line at the origin.]
The theory of algebraic curves, arguably the oldest branch of algebraic geometry, has seen major developments in recent years, for example in the study of syzygies, and around questions about moduli spaces and Hilbert schemes of curves. The theory is rich in research activity and unsolved problems. There is an encyclopedic work by Arbarello, Cornalba, Griffiths and Harris, but there is no modern text that could be used as a textbook and that goes beyond the basics of the theory. We have embarked on a project to write a book at roughly the level of the wonderful book on complex algebraic surfaces by Arnaud Beauville. The intent can be seen from a list of some major topics it will treat:
 Linear series and BrillNoether theory
 Personalities: curves in projective space with low genus and degree
 Overview of moduli and Jacobians
 Hilbert schemes
 Syzygies and linkage
The school will have two series of lectures, one by Harris and one by Eisenbud. Harris’ lectures will focus on the more geometric side of the theory, including BrillNoether theory, families of curves and Jacobians; while Eisenbud’s lectures will focus on the more algebraic side of the theory, including properties of the homogeneous coordinate rings of curves (CohenMacaulay, Gorenstein, free resolutions, scrolls, ...) Both lecturers will rely on chapters from the forthcoming book, which should be finished in large part by the time of the school. In addition, some of Eisenbud’s lectures will treat the use of Macaulay2 to investigate the projective embeddings of curves.
Updated on Aug 14, 2019 03:45 PM PDT 
Summer Graduate School Foundations and Frontiers of Probabilistic Proofs (Zurich, Switzerland)
Organizers: Alessandro Chiesa (University of California, Berkeley), Tom Gur (University of Warwick)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 complexitytheoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit localtoglobal 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 ultrafast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recentlydeployed technology, for example, as part of cryptographic constructions known as succinct noninteractive 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 cuttingedge research in this area.
Updated on Oct 14, 2019 10:12 AM PDT 
Summer Graduate School New Directions in Representation Theory (AMSI, Brisbane, Australia)
Organizers: Tim Brown (Australian Mathematical Sciences Institute), Joseph Grotowski (University of Queensland), Chloe Pearse (Australian Mathematical Sciences Institute), Jacqui Ramagge (University of Sydney), Ole Warnaar (University of Queensland), Geordie Williamson (University of Sydney)Representation Theory has undergone a revolution in recent years, with the development of what is now known as higher representation theory. In particular, the notion of categorification has led to the resolution of many problems previously considered to be intractable.
The school will begin by providing students with a brief but thorough introduction to what could be termed the “bread and butter of modern representation theory”, i.e., compact Lie groups and their representation theory; character theory; structure theory of algebraic groups.
We will then continue on to a number of more specialized topics. The final mix will depend on discussions with the prospective lecturers, but we envisage such topics as:
• modular representation theory of finite groups (blocks, defect groups, Broué’s conjecture);
• perverse sheaves and the geometric Satake correspondence;
• the representation theory of real Lie groups.
Updated on Aug 08, 2019 09:36 AM PDT 
Summer Graduate School Metric Geometry and Geometric Analysis (Oxford, United Kingdom)
Organizers: LEAD Cornelia Drutu (University of Oxford), Panos Papazoglou (University of Oxford)The purpose of the summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of nonsmooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.
All these themes are intertwined and have developed either together or greatly influencing one another. The summer school will introduce some of the latest developments and the remaining open problems in these very modern areas, and will emphasize their synergy.
Updated on Jul 31, 2019 11:07 AM PDT 
Summer Graduate School Sums of Squares Method in Geometry, Combinatorics and Optimization
Organizers: LEAD Grigoriy Blekherman (Georgia Institute of Technology), Annie Raymond (University of Massachusetts Amherst), Rekha Thomas (University of Washington)The study of nonnegative polynomials and sums of squares is a classical area of real algebraic geometry dating back to Hilbert’s 17th problem. It also has rich connections to real analysis via duality and moment problems. In the last 15 years, sums of squares relaxations have found a wide array of applications from very applied areas (e.g., robotics, computer vision, and machine learning) to theoretical applications (e.g., extremal combinatorics, theoretical computer science). Also, an intimate connection between sums of squares and classical algebraic geometry has been found. Work in this area requires a blend of ideas and techniques from algebraic geometry, convex geometry and representation theory. After an introduction to nonnegative polynomials, sums of squares and semidefinite optimization, we will focus on the following three topics:
 Sums of squares on real varieties (sets defined by real polynomial equations) and connections with classical algebraic geometry.
 Sums of squares method for proving graph density inequalities in extremal combinatorics. Here addition and multiplication take place in the gluing algebra of partially labelled graphs.
 Sums of squares relaxations for convex hulls of real varieties and thetabodies with applications in optimization.
The summer school will give a selfcontained introduction aimed at beginning graduate students, and introduce participants to the latest developments. In addition to attending the lectures, students will meet in intensive problem and discussion sessions that will explore and extend the topics developed in the lectures.
Updated on Jul 26, 2019 03:40 PM PDT 
Summer Graduate School Introduction to water waves
Organizers: Mihaela Ifrim (University of WisconsinMadison), Daniel Tataru (University of California, Berkeley)The purpose of this two weeks school is to introduce graduate students to the state of the art methods and results in the study of incompressible Euler’s equations in general, and water waves in particular. This is a research area which is highly relevant to many real life problems, and in which substantial progress has been made in the last decade.
The goal is to present the main current research directions in water waves. We will begin with the physical derivation of the equations, and present some of the analytic tools needed in study. The final goal will be twofold, namely (i) to understand the local solvability of the Cauchy problem for water waves, as well as (ii) to describe the long time behavior of solutions.
Through the lectures and associated problem sessions, students will learn about a number of new analysis tools which are not routinely taught in a graduate school curriculum. The goal is to help students acquire the knowledge needed in order to start research in water waves and Euler equations.
Updated on Jul 26, 2019 03:40 PM PDT 
Program Random and Arithmetic Structures in Topology
Organizers: Nicolas Bergeron (Université de Paris VI (Pierre et Marie Curie)), Jeffrey Brock (Yale University), Alexander Furman (University of Illinois at Chicago), Tsachik Gelander (Weizmann Institute of Science), Ursula Hamenstädt (Rheinische FriedrichWilhelmsUniversität Bonn), Fanny Kassel (Institut des Hautes Études Scientifiques (IHES)), LEAD Alan Reid (Rice University)The use of dynamical invariants has long been a staple of geometry and topology, from rigidity theorems, to classification theorems, to the general study of lattices and of the mapping class group. More recently, random structures in topology and notions of probabilistic geometric convergence have played a critical role in testing the robustness of conjectures in the arithmetic setting. The program will focus on invariants in topology, geometry, and the dynamics of group actions linked to random constructions.
Updated on Apr 22, 2019 01:56 PM PDT 
Program Decidability, definability and computability in number theory
Organizers: Valentina Harizanov (George Washington University), Maryanthe Malliaris (University of Chicago), Barry Mazur (Harvard University), Russell Miller (Queens College, CUNY; CUNY, Graduate Center), Jonathan Pila (University of Oxford), LEAD Thomas Scanlon (University of California, Berkeley), Alexandra Shlapentokh (East Carolina University), Carlos Videla (Mount Royal University)This program is focused on the twoway interaction of logical ideas and techniques, such as definability from model theory and decidability from computability theory, with fundamental problems in number theory. These include analogues of Hilbert's tenth problem, isolating properties of fields of algebraic numbers which relate to undecidability, decision problems around linear recurrence and algebraic differential equations, the relation of transcendence results and conjectures to decidability and decision problems, and some problems in anabelian geometry and field arithmetic. We are interested in this specific interface across a range of problems and so intend to build a semester which is both more topically focused and more mathematically broad than a typical MSRI program.
Updated on Oct 03, 2019 03:52 PM PDT 
Program Complementary Program 202021
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 Nov 20, 2019 01:47 PM PST 
Workshop Connections for Women: Decidability, definability and computability in number theory
Organizers: LEAD Valentina Harizanov (George Washington University), David Marker (University of Illinois, Chicago), Russell Miller (Queens College, CUNY; CUNY, Graduate Center), Jennifer Park (Ohio State University), Alexandra Shlapentokh (East Carolina University)The aim of the workshop is to discover how the problems in number theory and algebraic geometry arising from the Hilbert’s tenth problem for rationals interact with the ideas and techniques in mathematical logic, such as definability from model theory and decidability and degreetheoretic complexity from computability theory. This interaction includes various analogues of Hilbert’s tenth problem and related questions, focusing on the connections of algebraic, numbertheoretic, modeltheoretic, and computabilitytheoretic properties of structures and objects in algebraic number theory, anabelian geometry, field arithmetic, and differential algebra.
Updated on Apr 11, 2019 01:47 PM PDT 
Workshop Introductory Workshop: Decidability, definability and computability in number theory
Organizers: Maryanthe Malliaris (University of Chicago), Russell Miller (Queens College, CUNY; CUNY, Graduate Center), LEAD Jonathan Pila (University of Oxford), Alexandra Shlapentokh (East Carolina University)Our workshop will focus research efforts on the interaction of numbertheoretic questions with questions of decidability, definability, and computability, bringing together researchers approaching these questions from various sides to work on the core issues. This Introductory Workshop will serve as the introductory event of the MSRI semester program and is designed to introduce the basic structures and ideas of the different communities, and to highlight problems of active current interest.
Updated on Apr 23, 2019 01:30 PM PDT 
Workshop Connections for Women: Random and Arithmetic Structures in Topology
Organizers: LEAD Ursula Hamenstädt (Rheinische FriedrichWilhelmsUniversität Bonn), LEAD Fanny Kassel (Institut des Hautes Études Scientifiques (IHES))This twoday workshop will consist of various talks given by prominent female mathematicians in the field. These will be appropriate for graduate students, postdocs, and researchers in areas related to the program. The workshop will also include a professional development session.
This workshop is open to all mathematicians.
Updated on Jun 12, 2018 09:17 AM PDT 
Workshop Introductory Workshop: Random and Arithmetic Structures in Topology
Organizers: Jeffrey Brock (Yale University), Michelle Bucher (Université de Genève), LEAD Alan Reid (Rice University)The use of dynamical invariants has long been a staple of geometry and topology, from rigidity theorems, to classification theorems, to the general study of lattices and of the mapping class group. More recently, random structures in topology and notions of probabilistic geometric convergence have played a critical role in
testing the robustness of conjectures in the arithmetic setting.
In this introductory workshop, we will bring together junior and senior researchers in order to provide a mix of introductory lectures as well as reporting on more recent progress in topics from this diverse range of subjects.Updated on Jun 17, 2019 08:13 AM PDT 
Workshop Structure and randomness in locally symmetric spaces
Organizers: Nicolas Bergeron (Université de Paris VI (Pierre et Marie Curie)), Lewis Bowen (University of Texas, Austin), Tsachik Gelander (Weizmann Institute of Science), LEAD Alan Reid (Rice University), Abigail Thompson (University of California, Davis)The study of discrete subgroups of Lie groups and the associated locally symmetric manifolds has a long and rich history, with powerful interconnections between the geometry of the locally symmetric space, topology of towers of its finite covers, and numbertheoretic aspects. More recently dynamical and probabilistic techniques have been fruitfully employed to study these groups and spaces. The workshop will take stock of recent developments in these highly active fields from a variety of backgrounds.
Updated on Jun 06, 2019 09:08 AM PDT 
Program Mathematical problems in fluid dynamics
Organizers: Thomas Alazard (Ecole Normale Supérieure ParisSaclay; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Université ParisEst Créteil ValdeMarne; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of WisconsinMadison), Igor Kukavica (University of Southern California), David Lannes (Université de Bordeaux I; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)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 wellknown Euler equations for inviscid fluids, and the NavierStokes 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 Apr 25, 2019 02:32 PM PDT 
Workshop Recent Developments in Fluid Dynamics
Organizers: Thomas Alazard (Ecole Normale Supérieure ParisSaclay; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Université ParisEst Créteil ValdeMarne; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of WisconsinMadison), Igor Kukavica (University of Southern California), David Lannes (Université de Bordeaux I; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)The aim of the workshop is to bring together a broad array of researchers working on incompressible fluid dynamics. Some of the key topics to be covered are Euler flows, Navier Stokes equations as well as water wave flows and associated model equations. Some emphasis will also be placed on numerical analysis of the above evolutions.
Updated on Jun 18, 2019 09:54 AM PDT 
Program Universality 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 Washington), Alice Guionnet (École Normale Supérieure de Lyon), Alexander Its (Indiana UniversityPurdue University Indianapolis), Herbert Spohn (Technische Universität München), HorngTzer 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 24, 2019 03:08 PM PDT 
Workshop Integrable structures in random matrix theory and beyond
Organizers: LEAD Jinho Baik (University of Michigan), Alexei Borodin (Massachusetts Institute of Technology), Tamara Grava (University of Bristol; SISSA), Alexander Its (Indiana UniversityPurdue University Indianapolis), Sandrine Péché (Université de Paris VII (Denis Diderot))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, YangBaxter equation, KarlinMcGregor formula, Macdonald process, and stochastic six vertex model.
Updated on Jul 31, 2019 03:22 PM PDT 
Program 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), Eero Saksman (University of Helsinki), Fredrik Viklund (Royal Institute of Technology), JangMei Wu (University of Illinois at UrbanaChampaign)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 SchrammLoewner 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 
Program Complex 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 (Jacobs University Bremen), Mitsuhiro Shishikura (Kyoto University), Dylan Thurston (Indiana University)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
Past Scientific Events

Seminar MLA  Regular Seminar (part 1): Wave decay for starshaped waveguides
Updated on Nov 19, 2019 03:15 PM PST 
Seminar MLA  Special Seminar: Toeplitz operators, asymptotic Bergman projections, and second microlocalization
Updated on Nov 19, 2019 03:15 PM PST 
Seminar Iterated structures on manifolds working group: TBC
Created on Nov 14, 2019 11:19 AM PST 
Seminar HDMP  Physics: a guide for the perplexed: 2d quantum gravity and Witten's conjecture
Updated on Nov 08, 2019 03:18 PM PST 
Seminar Spectral networks reading group: TBA
Updated on Nov 08, 2019 08:28 AM PST 
Seminar HDMPLunch Q&A session
Updated on Nov 11, 2019 01:54 PM PST 
Seminar Topics in Differential Geometry (Chancellor Course)
Updated on Sep 26, 2019 04:41 PM PDT 
Seminar HDMPWeekly Seminar (Part 2): Symplectic properties of monodromy map for second order equation on a Riemann surface
Updated on Nov 11, 2019 09:10 AM PST 
Seminar MLA  Weekly Seminar (Part 2): Local rigidity of manifolds with hyperbolic cusps
Updated on Nov 11, 2019 09:11 AM PST 
Seminar MLA  Regular Seminar (part 2): Spectral gaps and uncertainty principles
Updated on Nov 07, 2019 04:49 PM PST 
Seminar Topics in Differential Geometry (Chancellor Course)
Updated on Sep 26, 2019 04:41 PM PDT 
Seminar HDMP  Weekly Seminar (Part 1): The JimboMiwaUeno tau function and its relationship to the Goldman Poisson structure and FockGoncharov parametrization
Updated on Nov 11, 2019 01:53 PM PST 
Seminar MLA  Weekly Seminar (Part 1): RuelleTaylor spectrum for Abelian Anosov actions
Updated on Nov 11, 2019 08:58 AM PST 
Seminar HDMP  Graduate Student Seminar (Part 1): Laminations, Trees and the Thurston compactification (Part 1)
Updated on Nov 11, 2019 09:13 AM PST 
Seminar MLA  Regular Seminar (part 1): On nondiffractive cones
Updated on Nov 11, 2019 08:57 AM PST 
Seminar HDMP  Graduate Student Seminar (Part 2): Laminations, Trees and the Thurston compactification (Part 2)
Updated on Nov 07, 2019 04:07 PM PST 
Seminar MLAGraduate Student Seminar: Geodesic XRay Transform on Asymptotically Hyperbolic Manifolds
Updated on Nov 07, 2019 01:58 PM PST 
Seminar Learning seminar on stability conditions: Fukaya categories of surfaces
Updated on Nov 07, 2019 02:53 PM PST 
Seminar Spectral networks reading group: Spectral network example session  part 2
Updated on Oct 30, 2019 02:54 PM PDT 
Seminar Working group seminar on spectral gaps: Introduction to resonancefree regions
Created on Nov 06, 2019 12:23 PM PST 
Seminar Topics in Differential Geometry (Chancellor Course)
Updated on Sep 26, 2019 04:40 PM PDT 
Seminar MLA  Regular Seminar (part 2): Feynman inverses of KleinGordon and wave operators
Updated on Oct 31, 2019 09:31 AM PDT 
Seminar HDMP  Physics: a guide for the perplexed: 2d4d systems and physics of spectral networks
Updated on Nov 04, 2019 04:17 PM PST 
Seminar MLA  Regular Seminar (part 1): Inverse problems in anisotropic elasticity and seismology
Updated on Oct 31, 2019 09:31 AM PDT 
Seminar HDMP  Weekly Seminar (Part 1): Topological recursions for volumes of the moduli space of Riemann surfaces
Updated on Oct 30, 2019 10:21 AM PDT 
Seminar HDMPWeekly Seminar (Part 2): Strata and Veech groups of porigamis
Updated on Nov 11, 2019 03:02 PM PST