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  1. Workshop Career in Academia

    Organizers: Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), Estelle Basor (AIM - American Institute of Mathematics), David Farmer (AIM - American Institute of Mathematics), Sally Koutsoliotas (Bucknell University)

    This workshop will focus on preparing each participant for a successful career as a mathematician at a college or university. Beginning with the hiring process, a thorough discussion of the various elements of the application packet will take place in the context of each participant's materials. Working individually with experienced faculty, participants will review and refine their cover letters, C.V., research, and teaching statements. This will be followed by activities related to the interview. The primary goals of the workshop are to develop an understanding of the hiring process from the institutions' perspective, to refine the application packet, to learn what to expect during the interview process (including the job talk), and to prepare for negotiating salary and start-up packages.

    Additional time will be spent on aspects of the pre-tenure years including the development of a research program, writing grant proposals, and mentoring research students. The three-day workshop will consist of one-on-one work with experienced mentors, small group discussions, critique of written materials, plenary sessions, and time for individual work and consultation.

    Updated on May 06, 2017 01:18 AM PDT
  2. Program Summer Research 2017

    Come spend time at MSRI in the summer! The Institute’s summer graduate schools and undergraduate program fill the lecture halls and some of the offices, but we have room for a modest number of visitors to come to do research singly or in small groups, while enjoying the excellent mathematical facilities, the great cultural opportunities of Berkeley, San Francisco and the Bay area, the gorgeous natural surroundings, and the cool weather.

    We can provide offices, library facilities and bus passes—unfortunately not financial support. Though the auditoria are largely occupied, there are blackboards and ends of halls, so 2-6 people could comfortably collaborate with one another. We especially encourage such groups to apply together.

    To make visits productive, we require at least a two-week commitment.  We strive for a wide mix of people, being sure to give special consideration to women, under-represented groups, and researchers from non-research universities. 

    Updated on Dec 20, 2016 03:16 PM PST
  3. Summer Graduate School Subfactors: planar algebras, quantum symmetries, and random matrices

    Organizers: LEAD Scott Morrison (Australian National University), Emily Peters (Loyola University), Noah Snyder (Indiana University)

    Subfactor theory is a subject from operator algebras, with many surprising connections to other areas of mathematics. This summer school will be devoted to understanding the representation theory of subfactors, with a particular emphasis on connections to quantum symmetries, fusion categories, planar algebras, and random matrices

    Updated on May 06, 2017 01:18 AM PDT
  4. MSRI-UP MSRI-UP 2017: Solving Systems of Polynomial Equations

    Organizers: LEAD Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Mercedes Franco (Queensborough Community College (CUNY)), Herbert Medina (Loyola Marymount University), Suzanne Weekes (Worcester Polytechnic Institute)

    The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
    In 2017, MSRI-UP will focus on Solving Systems of Polynomial Equations, a topic at the heart of almost every computational problem in the physical and life sciences. We will pay special attention to complexity issues, highlighting connections with tropical geometry, number theory, and the P vs. NP problem. The research program will be led by Prof. J. Maurice Rojas of Texas A&M University.
    Students who have had a linear algebra course and a course in which they have had to write proofs are eligible to apply. Due to funding restrictions, only U.S. citizens and permanent residents may apply regardless of funding. Members of underrepresented groups are especially encouraged to apply.

    Updated on Jan 03, 2017 04:10 PM PST
  5. Summer Graduate School Soergel Bimodules

    Organizers: LEAD Benjamin Elias (University of Oregon), Geordie Williamson (Max-Planck-Institut für Mathematik)

    We will give an introduction to categorical representation theory, focusing on the example of Soergel bimodules, which is a categorification of the Iwahori-Hecke algebra. We will give a comprehensive introduction to the "tool box" of modern (higher) representation theory: diagrammatics, homotopy categories, categorical diagonalization, module categories, Drinfeld center, algebraic Hodge theory.

    Updated on May 06, 2017 01:18 AM PDT
  6. Summer Graduate School Séminaire de Mathématiques Supérieures 2017: Contemporary Dynamical Systems

    Organizers: Sylvain Crovisier (Université de Paris VI (Pierre et Marie Curie)-Université de Paris XI (Paris-Sud)), LEAD Konstantin Khanin (University of Toronto), Andrés Navas Flores (University of Santiago de Chile), Christiane Rousseau (Université de Montréal), Marcelo Viana (Institute of Pure and Applied Mathematics (IMPA)), Amie Wilkinson (University of Chicago)

    The theory of dynamical systems has witnessed very significant developments in the last decades, includi​n​g the work of two 2014 Fields medalists, Artur Avila and Maryam Mirzakhani. ​The school will concentrate on the recent significant developments in the field of dynamical systems and present some of the present main streams of research. Two central themes will be those of partial hyperbolicity on one side, and rigidity, group actions and renormalization on the other side.​ ​Other themes will ​include homogeneous dynamics and geometry and dynamics on infinitely flat surfaces (both providing connections to the work of Maryam Mirzakhani), topological dynamics, thermodynamical formalism, singularities and bifurcations in analytic dynamical systems.  

    Updated on May 06, 2017 01:18 AM PDT
  7. Summer Graduate School Positivity Questions in Geometric Combinatorics

    Organizers: Eran Nevo (The Hebrew University of Jerusalem), Raman Sanyal (Johann Wolfgang Goethe-Universität Frankfurt)

    McMullen’s g-Conjecture from 1970 is a shining example of mathematical foresight that combined all results available at that time to conjure a complete characterization of face numbers of convex simple/simplicial polytopes. The key statement in its verification is that certain combinatorial numbers associated to geometric (or topological) objects are non-negative. The aim of this workshop is to introduce graduate students to selected contemporary topics in geometric combinatorics with an emphasis on positivity questions. It is fascinating that the dual notions of simple and simplicial polytopes lead to different but equally powerful algebraic frameworks to treat such questions. A key feature of the lectures will be the simultaneous development of these algebraic frameworks from complementary perspectives: combinatorial-topological and convex-geometric.  General concepts (such as Lefschetz elements, Hodge–Riemann–Minkowski inequalities) will be developed side-by-side, and analogies will be drawn to concepts in algebraic geometry, Fourier analysis, rigidity theory and measure theory. This allows for entry points for students with varying backgrounds.  The courses will be supplemented with guest lectures highlighting further connections to other fields.

    Updated on May 06, 2017 01:18 AM PDT
  8. Summer Graduate School Nonlinear dispersive PDE, quantum many particle systems and the world between

    Organizers: Natasa Pavlovic (University of Texas), Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)

    The purpose of the summer school is to introduce graduate students to the recent developments in the area of dispersive partial differential equations (PDE), which have received a great deal of attention from mathematicians, in part due to ubiquitous applications to nonlinear optics, water wave theory and plasma physics.

    Recently remarkable progress has been made in understanding existence and uniqueness of solutions to nonlinear Schrodinger (NLS) and KdV equations, and properties of those solutions. We will outline the basic tools that were developed to address these questions. Also we will present some of recent results on derivation of NLS equations from quantum many particle systems and will discuss how methods developed to study the NLS can be relevant in the context of the derivation of this nonlinear equation.

    Updated on May 06, 2017 01:18 AM PDT
  9. Summer Graduate School Automorphic Forms and the Langlands Program

    Organizers: LEAD Kevin Buzzard (Imperial College, London)

    The summer school will be an introduction to the more algebraic aspects of the theory of automorphic forms and representations. One of the goals will be to understand the statements of the main conjectures in the Langlands programme. Another will be to gain a good working understanding of the fundamental definitions in the theory, such as principal series representations, the Satake isomorphism, and of course automorphic forms and representations for groups such as GL_n and its inner forms.

    Updated on May 06, 2017 01:18 AM PDT
  10. Program Geometric and Topological Combinatorics

    Organizers: Jesus De Loera (University of California, Davis), Victor Reiner (University of Minnesota Twin Cities), LEAD Francisco Santos (University of Cantabria), Francis Su (Harvey Mudd College), Rekha Thomas (University of Washington), Günter M. Ziegler (Freie Universität Berlin)

    Combinatorics is one of the fastest growing areas in contemporary Mathematics, and much of this growth is due to the connections and interactions with other areas of Mathematics. This program is devoted to the very vibrant and active area of interaction between Combinatorics with Geometry and Topology. That is, we focus on (1) the study of the combinatorial properties or structure of geometric and topological objects and (2) the development of geometric and topological techniques to answer combinatorial problems.

    Key examples of geometric objects with intricate combinatorial structure are point configurations and matroids, hyperplane and subspace arrangements, polytopes and polyhedra, lattices, convex bodies, and sphere packings. Examples of topology in action answering combinatorial challenges are the by now classical Lovász’s solution of the Kneser conjecture, which yielded functorial approaches to graph coloring, and the  more recent, extensive topological machinery leading to breakthroughs on Tverberg-type problems.

    Updated on Jul 05, 2016 08:46 AM PDT
  11. Program Geometric Functional Analysis and Applications

    Organizers: Franck Barthe (Université de Toulouse III (Paul Sabatier)), Marianna Csornyei (University of Chicago), Boaz Klartag (Weizmann Institute of Science), Alexander Koldobsky (University of Missouri), Rafal Latala (University of Warsaw), LEAD Mark Rudelson (University of Michigan)

    Geometric functional analysis lies at the interface of convex geometry, functional analysis and probability. It has numerous applications ranging from geometry of numbers and random matrices in pure mathematics to geometric tomography and signal processing in engineering and numerical optimization and learning theory in computer science.

    One of the directions of the program is classical convex geometry, with emphasis on connections with geometric tomography, the study of geometric properties of convex bodies based on information about their sections and projections. Methods of harmonic analysis play an important role here. A closely related direction is asymptotic geometric analysis studying geometric properties of high dimensional objects and normed spaces, especially asymptotics of their quantitative parameters as dimension tends to infinity. The main tools here are concentration of measure and related probabilistic results. Ideas developed in geometric functional analysis have led to progress in several areas of applied mathematics and computer science, including compressed sensing and random matrix methods. These applications as well as the problems coming from computer science will be also emphasised in our program.

    Updated on Jan 24, 2017 07:35 PM PST
  12. Workshop Connections for Women: geometry and probability in high dimensions

    Organizers: LEAD Shiri Artstein (Tel Aviv University), Marianna Csornyei (University of Chicago), Eva Kopecka (University of Innsbruck), Elisabeth Werner (Case Western Reserve University)

    This workshop will be on topics connected with Asymptotic Geometric Analysis - a relatively new field, the young finite dimensional cousin of Banach Space theory, functional analysis and classical convexity. We study high, but finite, dimensional objects, where the disorder of many parameters and many dimensions is regularized by convexity assumptions.  This workshop is open to all mathematicians.

    Updated on May 06, 2017 01:18 AM PDT
  13. Workshop Introductory Workshop: phenomena in high dimensions

    Organizers: Alexander Koldobsky (University of Missouri), Michel Ledoux (University of Toulouse), Monika Ludwig (Technische Universität Wien), Alain Pajor (Université de Paris Est Marne-la-Vallée), Stanislaw Szarek (Case Western Reserve University), LEAD Roman Vershynin (University of Michigan)

    This workshop will consist of several short courses related to high dimensional convex geometry, high dimensional probability, and applications in data science. The lectures will be accessible for graduate students.

    Updated on May 06, 2017 01:18 AM PDT
  14. Workshop Connections for Women Workshop: Geometric and Topological Combinatorics

    Organizers: Federico Ardila (San Francisco State University), Margaret Bayer (University of Kansas), Francisco Santos (University of Cantabria), LEAD Cynthia Vinzant (North Carolina State University)

    This workshop will feature lectures on a variety of topics in geometric and topological combinatorics, given by prominent women and men in the field. 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 May 06, 2017 01:18 AM PDT
  15. Workshop Introductory Workshop: Geometric and Topological Combinatorics

    Organizers: Imre Barany (Hungarian Academy of Sciences (MTA)), Anders Björner (Royal Institute of Technology (KTH)), LEAD Ben Braun (University of Kentucky), Isabella Novik (University of Washington), Francis Su (Harvey Mudd College), Rekha Thomas (University of Washington)

    The introductory workshop will present the main topics that will be the subject of much of the Geometric and Topological Combinatorics Program at MSRI.  Key areas of interest are point configurations and matroids, hyperplane and subspace arrangements, polytopes and polyhedra, lattices, convex bodies, and sphere packings. This workshop will consist of introductory talks on a variety of topics, intended for a broad audience. 

    Updated on May 06, 2017 01:18 AM PDT
  16. Workshop Geometric and topological combinatorics: Modern techniques and methods

    Organizers: Patricia Hersh (North Carolina State University), LEAD Victor Reiner (University of Minnesota Twin Cities), Bernd Sturmfels (University of California, Berkeley), Frank Vallentin (Universität zu Köln), Günter M. Ziegler (Freie Universität Berlin)

    This workshop will focus on the interaction between Combinatorics, Geometry and Topology, including recent developments and techniques in areas such as 

    -- polytopes and cell complexes,
    -- simplicial complexes and higher order graph theory,
    -- methods from equivariant topology and configuration spaces,

    -- geometric combinatorics in optimization and social choice theory,
    -- algebraic and algebro-geometric methods.

    Updated on May 06, 2017 01:18 AM PDT
  17. Workshop Modern Math Workshop 2017

    Organizers: Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), Leslie McClure (SAMSI - Statistical and Applied Mathematical Sciences Institute), Christian Ratsch (University of California, Los Angeles; Institute of Pure and Applied Mathematics (IPAM)), Ulrica Wilson (Morehouse College; Institute for Computational and Experimental Research in Mathematics (ICERM))

    As part of the Mathematical Sciences Collaborative Diversity Initiatives, nine mathematics institutes are pleased to offer their annual SACNAS pre-conference event, the 2017 Modern Math Workshop (MMW). The Modern Math Workshop is intended to encourage minority undergraduates to pursue careers in the mathematical sciences and to assist undergraduates, graduate students and recent PhDs in building their research networks. The Modern Math Workshop is part of the SACNAS National Conference; the workshop and the conference take place in the Salt Palace Convention Center in Salt Lake City, Utah. The MMW starts at 1:00 pm on Wednesday, October 18 with registration beginning at noon.

    Updated on May 18, 2017 10:37 AM PDT
  18. Workshop Geometric functional analysis and applications

    Organizers: Franck Barthe (Université de Toulouse III (Paul Sabatier)), Rafal Latala (University of Warsaw), Emanuel Milman (Technion---Israel Institute of Technology), Assaf Naor (Princeton University), LEAD Gideon Schechtman (Weizmann Institute of Science)

    This is the main workshop of the program "Geometric functional analysis and applications". It will focus on the main topics of the program. These include: Convex geometry, Asymptotic geometric analysis, Interaction with computer science, Signal processing, Random matrix theory and other aspects of Probability.

    Updated on May 06, 2017 01:18 AM PDT
  19. Workshop Women in Topology

    Organizers: Maria Basterra (University of New Hampshire), Kristine Bauer (University of Calgary), LEAD Kathryn Hess (École Polytechnique Fédérale de Lausanne (EPFL)), Brenda Johnson (Union College--Union University)

    The Women in Topology (WIT) network is an international group of female mathematicians interested in homotopy theory whose main goal is to increase the retention of women in the field by providing both unique collaborative research opportunities and mentorship between colleagues.  The MSRI WIT meeting will be organized as an afternoon of short talks from participants, followed by two days of open problem seminars and working groups designed to stimulate new collaborations, as well as to strengthen those already ongoing among the participants

    Updated on May 06, 2017 01:18 AM PDT
  20. Program Enumerative Geometry Beyond Numbers

    Organizers: Mina Aganagic (University of California, Berkeley), Denis Auroux (University of California, Berkeley), Jim Bryan (University of British Columbia), LEAD Andrei Okounkov (Columbia University), Balazs Szendroi (University of Oxford)

    Traditional enumerative geometry asks certain questions to which the expected answer is a number: for instance, the number of lines incident with two points in the plane (1, Euclid), or the number of twisted cubic curves on a quintic threefold (317 206 375). It has however been recognized for some time that the numerics is often just the tip of the iceberg: a deeper exploration reveals interesting geometric, topological, representation-, or knot-theoretic structures. This semester-long program will be devoted to these hidden structures behind enumerative invariants, concentrating on the core fields where these questions start: algebraic and symplectic geometry.

    Updated on Oct 12, 2015 03:39 PM PDT
  21. Program Group Representation Theory and Applications

    Organizers: Robert Guralnick (University of Southern California), Alexander Kleshchev (University of Oregon), Gunter Malle (TU Kaiserslautern), Gabriel Navarro (University of Valencia), Julia Pevtsova (University of Washington), Raphael Rouquier (University of California, Los Angeles), LEAD Pham Tiep (University of Arizona)

    Group Representation Theory is a central area of Algebra, with important and deep connections to areas as varied as topology, algebraic geometry, number theory, Lie theory, homological algebra, and mathematical physics. Born more than a century ago, the area still abounds with basic problems and fundamental conjectures, some of which have been open for over five decades. Very recent breakthroughs have led to the hope that some of these conjectures can finally be settled. In turn, recent results in group representation theory have helped achieve substantial progress in a vast number of applications.

    The goal of the program is to investigate all these deep problems and the wealth of new results and directions, to obtain major progress in the area, and to explore further applications of group representation theory to other branches of mathematics.

    Updated on Mar 16, 2016 01:25 PM PDT
  22. Workshop Connections for Women: Enumerative Geometry Beyond Numbers

    Organizers: Barbara Fantechi (Sissa), LEAD Chiu-Chu Melissa Liu (Columbia University)

    This two-day workshop will provide an overview of significant developments and open problems in modern enumerative geometry, from the perspectives of both algebraic geometry and symplectic topology. 

    This workshop is open to all mathematicians.

    Updated on May 24, 2017 01:10 PM PDT
  23. Workshop Introductory Workshop: Enumerative Geometry Beyond Numbers

    Organizers: Denis Auroux (University of California, Berkeley), LEAD Chiu-Chu Melissa Liu (Columbia University), Andrei Okounkov (Columbia University)

    This workshop will consist of expository mini-courses and lectures introducing various aspects of modern enumerative geometry, among which: enumeration via intersection theory on moduli spaces of curves or sheaves, including Gromov-Witten and Donaldson-Thomas invariants; motivic and K-theoretic refinement of these invariants; and categorical invariants (derived categories of coherent sheaves, Fukaya categories).

    Updated on May 06, 2017 01:18 AM PDT
  24. Workshop Connections for Women: Group Representation Theory and Applications

    Organizers: Karin Erdmann (University of Oxford), Julia Pevtsova (University of Washington)

    This intensive two day workshop will introduce graduate students and recent PhD’s to some current topics of research in Representation Theory. It will consists of a mixture of survey talks on the hot topics in the area given by leading experts and research talks by junior mathematicians covering subjects such as new developments in character theory, group cohomology, representations of Lie algebras and algebraic groups, geometric representation theory, and categorification. 

    Updated on May 06, 2017 01:18 AM PDT
  25. Workshop Introductory Workshop: Group Representation Theory and Applications

    Organizers: Robert Guralnick (University of Southern California), Gunter Malle (TU Kaiserslautern)

    The workshop will survey various important and active areas of the representation theory of finite and algebraic groups, and introduce the audience to several basic open problems in the area. It will consist of 6 series of 3 lectures each given by top experts in the field. The lectures are designed for a diverse audience and will be accessible to non-specialists and graduate students with some background in representation theory. Topics covered include Representation theory of algebraic groups, Decomposition numbers of finite groups of Lie type, Deligne-Lusztig theory,  Block theory, Categorification, and Local-global-conjectures.

    Updated on May 06, 2017 01:18 AM PDT
  26. Workshop The Homological Conjectures: Resolved!

    Organizers: Bhargav Bhatt (University of Michigan), Srikanth Iyengar (University of Utah), Wieslawa Niziol (CNRS, ENS-Lyon), LEAD Anurag Singh (University of Utah)

    The homological conjectures in commutative algebra are a network of conjectures that have generated a tremendous amount of activity in the last 50 years. They had largely been resolved for commutative rings that contain a field, but, with the exception of some low dimensional cases, several remained open in mixed characteristic --- until recently, when Yves André announced a proof of Hochster's Direct Summand Conjecture. The progress comes from systematically applying Scholze's theory of perfectoid spaces, which had already shown its value by solving formidable problems in number theory and representation theory. One of the goals of the workshop is to cover the ingredients going into the proofs of the Direct Summand Conjecture.

    Updated on May 23, 2017 09:48 AM PDT
  27. Workshop Structures in Enumerative Geometry

    Organizers: Mina Aganagic (University of California, Berkeley), Jim Bryan (University of British Columbia), LEAD Davesh Maulik (Massachusetts Institute of Technology), Balazs Szendroi (University of Oxford), Richard Thomas (Imperial College, London)

    The purpose of the workshop is to bring together specialists to work on understanding the many-faceted mathematical structures underlying problems in enumerative geometry. Topics represented at the workshop will include: geometric representation theory, supersymmetric gauge theory, string theory, knot theory, and derived geometry, all of which have had a profound effect on the development of modern enumerative geometry.

    Updated on May 23, 2017 09:49 AM PDT
  28. Workshop Representations of Finite and Algebraic Groups

    Organizers: Robert Guralnick (University of Southern California), Alexander Kleshchev (University of Oregon), Gunter Malle (TU Kaiserslautern), Gabriel Navarro (University of Valencia), LEAD Pham Tiep (University of Arizona)

    The workshop will bring together key researchers working in various areas of Group Representation Theory to strengthen the interaction and collaboration between them and to make further progress on a number of basic problems and conjectures in the field. Topics of the workshop include
    -- Global-local conjectures in the representation theory of finite groups
    -- Representations and cohomology of simple, algebraic and finite groups
    -- Connections to Lie theory and categorification, and
    -- Applications to group theory, number theory, algebraic geometry, and combinatorics.

    Updated on May 26, 2017 03:27 PM PDT
  29. Summer Graduate School H-principle

    Organizers: Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tsukuba)

    Created on May 15, 2017 11:01 AM PDT
  30. Program Hamiltonian systems, from topology to applications through analysis

    Organizers: Rafael de la Llave (Georgia Institute of Technology), LEAD Albert Fathi (École Normale Supérieure de Lyon), Vadim Kaloshin (University of Maryland), Robert Littlejohn (University of California, Berkeley), Philip Morrison (University of Texas at Austin), Tere M. Seara (Universitat Politecnica de Catalunya), Serge Tabachnikov (Pennsylvania State University), Amie Wilkinson (University of Chicago)

    The interdisciplinary nature of Hamiltonian systems is deeply ingrained in its history. Therefore the program will bring together the communities of mathematicians with the community of practitioners, mainly engineers, physicists, and theoretical chemists who use Hamiltonian systems daily. The program will cover not only the mathematical aspects of Hamiltonian systems but also their applications, mainly in space mechanics, physics and chemistry.

    The mathematical aspects comprise celestial mechanics, variational methods, relations with PDE, Arnold diffusion and computation. The applications concern celestial mechanics, astrodynamics, motion of satellites, plasma physics, accelerator physics, theoretical chemistry, and atomic physics.

    The goal of the program is to bring to the forefront both the theoretical aspects and the applications, by making available for applications the latest theoretical developments, and also by nurturing the theoretical mathematical aspects with new problems that come from concrete problems of applications.

    Updated on Mar 16, 2017 03:08 PM PDT
  31. Workshop Connections for Women: Hamiltonian Systems, from topology to applications through analysis

    Organizers: Marie-Claude Arnaud (Université d'Avignon), LEAD Basak Gurel (University of Central Florida), Tere M. Seara (Universitat Politecnica de Catalunya)

    This workshop will feature lectures on a variety of topics in Hamiltonian dynamics given by leading researchers in the area. The talks will focus on recent developments in subjects closely related to the program such as Arnold diffusion, celestial mechanics, Hamilton-Jacobi equations, KAM methods, Aubry-Mather theory and symplectic topological techniques, and on applications. The workshop is open to all mathematicians in areas related to the program.

    Updated on May 06, 2017 01:18 AM PDT
  32. Program Derived Algebraic Geometry

    Organizers: Julie Bergner (University of Virginia), LEAD Bhargav Bhatt (University of Michigan), Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), Nikita Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Bertrand Toen (Centre National de la Recherche Scientifique (CNRS)), Gabriele Vezzosi (Università di Firenze)

    Derived algebraic geometry is an extension of algebraic geometry that provides a convenient framework for directly treating non-generic geometric situations (such as non-transverse intersections in intersection theory), in lieu of the more traditional perturbative approaches (such as the “moving” lemma). This direct approach, in addition to being conceptually satisfying, has the distinct advantage of preserving the symmetries of the situation, which makes it much more applicable. In particular, in recent years, such techniques have found applications in diverse areas of mathematics, ranging from arithmetic geometry, mathematical physics, geometric representation theory, and homotopy theory. This semester long program will be dedicated to exploring these directions further, and finding new connections.

    Updated on Nov 02, 2016 04:30 PM PDT
  33. Program Birational Geometry and Moduli Spaces

    Organizers: Antonella Grassi (University of Pennsylvania), LEAD Christopher Hacon (University of Utah), Sándor Kovács (University of Washington), Mircea Mustaţă (University of Michigan), Martin Olsson (University of California, Berkeley)

    Birational Geometry and Moduli Spaces are two important areas of Algebraic Geometry that have recently witnessed a flurry of activity and substantial progress on many fundamental open questions. In this program we aim to  bring together key researchers in these and related areas to highlight the recent exciting progress and to explore future avenues of research.
    This program will focus on the following themes: Geometry and Derived Categories, Birational Algebraic Geometry, Moduli Spaces of Stable Varieties, Geometry in Characteristic p>0, and Applications of Algebraic Geometry: Elliptic Fibrations of Calabi-Yau Varieties in Geometry, Arithmetic and the Physics of String Theory

    Updated on Jan 31, 2017 07:46 PM PST
  34. Workshop Connections for Women: Derived Algebraic Geometry, Birational Geometry and Moduli Spaces

    Organizers: Julie Bergner (University of Virginia), LEAD Antonella Grassi (University of Pennsylvania), Bianca Viray (University of Washington), Kirsten Wickelgren (Georgia Institute of Technology)

    This workshop will be on different aspects of Algebraic Geometry relating Derived Algebraic Geometry and Birational Geometry. In particular the workshop will focus on connections to other branches of mathematics and open problems. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.

    Updated on May 06, 2017 01:18 AM PDT
  35. Workshop Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces

    Organizers: Julie Bergner (University of Virginia), Bhargav Bhatt (University of Michigan), Christopher Hacon (University of Utah), LEAD Mircea Mustaţă (University of Michigan), Gabriele Vezzosi (Università di Firenze)

    The workshop will survey several areas of algebraic geometry, providing an introduction to the two main programs hosted by MSRI in Spring 2019. It will consist of 6 expository mini-courses and 8 separate lectures, each given by top experts in the field. 

    The focus of the workshop will be the recent progress in derived algebraic geometry, birational geometry and moduli spaces. The lectures will be aimed at a wide audience including advanced graduate students and postdocs with a background in algebraic geometry.

    Updated on May 06, 2017 01:18 AM PDT
  36. Workshop Derived algebraic geometry and its applications

    Organizers: Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), LEAD Nikita Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Brooke Shipley (University of Illinois at Chicago), Bertrand Toen (Centre National de la Recherche Scientifique (CNRS))

    This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.    

    Updated on May 06, 2017 01:18 AM PDT
  37. Workshop Recent Progress in Moduli Theory

    Organizers: Lucia Caporaso (University of Rome, Roma 3), LEAD Sándor Kovács (University of Washington), Martin Olsson (University of California, Berkeley)

    This workshop will be focused on presenting the latest developments in moduli theory, including (but not restricted to) recent advances in compactifications of moduli spaces of higher dimensional varieties, the birational geometry of moduli spaces, abstract methods including stacks, stability criteria, and applications in other disciplines. 

    Updated on May 06, 2017 01:18 AM PDT
  38. Program Holomorphic Differentials in Mathematics and Physics

    Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at Urbana-Champaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas), Anna Wienhard (Ruprecht-Karls-Universität 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 Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called 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 low-dimensional 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 Feb 16, 2017 03:58 PM PST
  39. Program Microlocal Analysis

    Organizers: Pierre Albin (University of Illinois at Urbana-Champaign), Nalini Anantharaman (Université de Strasbourg), Kiril Datchev (Purdue University), Raluca Felea (Rochester Institute of Technology), Colin Guillarmou (École Normale Supérieure), 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 Feb 21, 2017 10:35 AM PST