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Upcoming Scientific Events

  1. Seminar Applied fluids

    Updated on Jan 14, 2021 06:36 AM PST
  2. Seminar Applied fluids

    Updated on Jan 14, 2021 06:36 AM PST
  3. Seminar Applied fluids

    Updated on Jan 14, 2021 06:36 AM PST
  4. Seminar Applied fluids

    Updated on Jan 14, 2021 06:36 AM PST
  5. Seminar Applied fluids

    Updated on Jan 14, 2021 06:36 AM PST
  6. Workshop [Moved Online] Recent Developments in Fluid Dynamics

    Organizers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Laboratoire Jacques-Louis Lions; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of Wisconsin-Madison), Igor Kukavica (University of Southern California), David Lannes (Institut de Mathématiques de Bordeaux; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)
    Valuri
    Water waves

    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 Mar 01, 2021 06:54 AM PST
  7. Seminar Applied fluids

    Updated on Jan 14, 2021 06:37 AM PST
  8. Seminar Applied fluids

    Updated on Jan 14, 2021 06:37 AM PST
  9. Workshop [Moved Online] Critical Issues in Mathematics Education 2021: Initiating, Sustaining, and Researching Mathematics Department Transformation of Introductory Courses for STEM Majors

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

    NOTE: The introductory sessions for this workshop will be held online the morning of April 29th.  Additional sessions will be held when it is once again possible to meet in person.  Times listed on schedule is in Pacfic Standard Time.

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

    Speaker Abstracts

    Updated on Feb 22, 2021 09:57 AM PST
  10. Seminar Applied fluids

    Updated on Jan 14, 2021 06:37 AM PST
  11. Workshop [Moved Online] Hot Topics: Topological Insights in Neuroscience

    Organizers: Carina Curto (Pennsylvania State University), Chad Giusti (University of Delaware), LEAD Kathryn Hess (École Polytechnique Fédérale de Lausanne (EPFL)), Ran Levi (University of Aberdeen)
    2020 21 topological insights neuroscience image hess.2019.02.27
    Image created by Nicolas Antille, of the visualization team of the Blue Brain Project at EPFL

    This workshop will be held online May 4-7 and May 10-11, 2021. The Zoom link will be provided at a later time. You must register for the workshop to receive the password.  The workshop is held in Pacific Standard Time.

    The talks in this workshop will present a wide array of current applications of topology in neuroscience, including classification and synthesis of neuron morphologies, analysis of synaptic plasticity, algebraic analysis of the neural code, topological analysis of neural networks and their dynamics, topological decoding of neural activity, diagnosis of traumatic brain injuries, and topological biomarkers for psychiatric disease. Some of the talks will be devoted to promising new directions in algebraic topology that have been inspired by neuroscience.

    Updated on Feb 10, 2021 04:31 PM PST
  12. Summer Graduate School Séminaire de Mathématiques Supérieures 2021: Microlocal Analysis: Theory and Applications (Virtual School)

    Organizers: Suresh Eswarathasan (Dalhousie University), Dmitry Jakobson (McGill University), Katya Krupchyk (University of California, Irvine), Stephane Nonnenmacher (Université de Paris XI)

    Microlocal analysis originated in the study of linear partial differential equations (PDEs) in the high-frequency regime, through a combination of ideas from Fourier analysis and classical Hamiltonian mechanics. In parallel, similar ideas and methods had been developed since the early times of quantum mechanics, the smallness of Planck’s constant allowing to use semiclassical methods. The junction between these two points of view (microlocal and semiclassical) only emerged in 1970s, and has taken its full place in the PDE community in the last 20 years. This methodology resulted in major advances in the understanding of linear and nonlinear PDEs in the last 50 years. Moreover, microlocal methods continue to find new applications in diverse areas of mathematical analysis, such as the spectral theory of nonselfadjoint operators, scattering theory, and inverse problems.

    Updated on Dec 01, 2020 02:04 PM PST
  13. Seminar Applied fluids

    Updated on Jan 14, 2021 06:37 AM PST
  14. Seminar Applied fluids

    Updated on Jan 14, 2021 06:37 AM PST
  15. Seminar Applied fluids

    Updated on Jan 14, 2021 06:38 AM PST
  16. Summer Graduate School 2021 CRM-PIMS Summer School in Probability (CRM, Montreal)

    Organizers: LEAD Louigi Addario-Berry (McGill University), Omer Angel (University of British Columbia), Alexander Fribergh (University of Montreal), Mathav Murugan (University of British Columbia), Edwin Perkins (University of British Columbia)
    Image
    The Sherrington-Kirkpatrick model, aka the randomly-weighted complete graph. Edge weights are indicated using grayscale. Six distinguished vertices have been randomly chosen; edges between those vertices are shaded black to form a "hidden signal".

    The courses in this summer school focus on mathematical models of group dynamics, how to describe their dynamics and their scaling limits, and the connection to discrete and continuous optimization problems.

    The phrase "group dynamics" is used loosely here -- it may refer to species migration, the spread of a virus, or the propagation of electrons through an inhomogeneous medium, to name a few examples. Very commonly, such systems can be described via stochastic processes which approximately behave like the solution of an appropriate partial differential equation in the large-population limit.

    Updated on Jan 04, 2021 11:52 AM PST
  17. Seminar Applied fluids

    Updated on Jan 14, 2021 06:38 AM PST
  18. Summer Research in Mathematics 2021 Summer Research in Mathematics

    Due to the pandemic, the 2019 Summer Research in Mathematics program was postponed to 2020.  Therefore, MSRI is not accepting new applications at this time.

    MSRI's Summer Research in Mathematics program provides space, funding, and the opportunity for in-person collaboration to small groups of mathematicians, especially women and gender-expansive individuals, whose ongoing research may have been disproportionately affected by various obstacles including family obligations, professional isolation, or access to funding. Through this effort, MSRI aims to mitigate the obstacles faced by these groups, improve the odds of research project completion, and deepen their research experience.

    The ultimate goal of this program is to enhance the mathematical sciences as a whole by positively affecting the research and careers of all of its participants and assisting their efforts to maintain involvement in the research community.

    Updated on Aug 31, 2020 11:43 AM PDT
  19. Summer Graduate School Sparsity of Algebraic Points

    Organizers: Philipp Habegger (University of Basel), LEAD Hector Pasten (Pontificia Universidad Católica de Chile)
    Sgspic
    The Corvaja-Zannier proof of Siegel's theorem using subspaces. Illustrated by Sofía Pastén Vásquez.

    The theory of Diophantine equations is understood today as the study of algebraic points in algebraic varieties, and it is often the case that algebraic points of arithmetic relevance are expected to be sparse.

    This summer school will introduce the participants to two of the main techniques in the subject: (i) the filtration method to prove algebraic degeneracy of integral points by means of the subspace theorem, leading to special cases of conjectures by Bombieri, Lang, and Vojta, and (ii) unlikely intersections through o-minimality and bi-algebraic geometry, leading to results in the context of the Manin-Mumford conjecture, the André-Oort conjecture, and generalizations. This SGS should provide an entry point to a very active research area in modern number theory.

    Updated on Sep 15, 2020 04:26 PM PDT
  20. Workshop [Online] Workshop on Mathematics and Racial Justice

    Organizers: Caleb Ashley (Boston College), Ron Buckmire (Occidental College), Duane Cooper (Morehouse College), Erica Graham (Bryn Mawr College), Monica Jackson (American University), LEAD Omayra Ortega (Sonoma State University), LEAD Robin Wilson (California State Polytechnic University, Pomona)

    The overarching goal of the Workshop on Mathematics and Racial Justice is to explore the role that mathematics plays in today’s movement for racial justice. For the purposes of this workshop, racial justice is the result of intentional, active and sustained anti-racist practices that identify and dismantle racist structures and policies that operate to oppress, disenfranchise, harm, and devalue Black people. This workshop will bring together mathematicians, statisticians, computer scientists, and STEM educators as well as members of the general public interested in using the tools of these disciplines to critically examine and eradicate racial disparities in society. Researchers with expertise or interest in problems at the intersection of mathematics, statistics and racial justice are encouraged to participate. This workshop will take place over two weeks and will include sessions on Bias in Algorithms and Technology; Fair Division, Allocation, and Representation; Public Health Disparities; and Racial Inequities in Mathematics Education.

    Updated on Feb 24, 2021 04:20 PM PST
  21. MSRI-UP MSRI-UP 2021: Parking Functions: Choose your own adventure

    Organizers: Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI - Mathematical Sciences Research Institute), LEAD Rebecca Garcia (Sam Houston State University), Pamela Harris (Williams College), Candice Price (Smith College)

    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 2021, MSRI-UP will focus on Parking Functions: Choose your own adventure. The research program will be led by Dr. Pamela E. Harris, Associate Professor of Mathematics at Williams College.

    Updated on Feb 05, 2021 01:42 PM PST
  22. Summer Graduate School Mathematics of Big Data: Sketching and (Multi-) Linear Algebra

    Organizers: LEAD Kenneth Clarkson (IBM Research Division), Lior Horesh (IBM Thomas J. Watson Research Center)
    Image %281%29

    This summer school will introduce graduate students to sketching-based approaches to computational linear and multi-linear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.

    Updated on Aug 04, 2020 09:38 AM PDT
  23. Summer Graduate School [POSTPONED] 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 non-smooth 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 Feb 03, 2021 03:04 PM PST
  24. Summer Graduate School Gauge Theory in Geometry and Topology

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

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

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

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

    Updated on Dec 23, 2020 12:30 PM PST
  25. Summer Graduate School Random Conformal Geometry

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

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

    Updated on Aug 04, 2020 10:24 AM PDT
  26. Summer Graduate School Foundations and Frontiers of Probabilistic Proofs (Zurich, Switzerland)

    Organizers: Alessandro Chiesa (University of California, Berkeley), Tom Gur (University of Warwick)
    Proofs main logo
    Several executions of a 3-dimensional sumcheck protocol with a random order of directions (thanks to Dev Ojha for creating the diagram)

    Proofs are at the foundations of mathematics. Viewed through the lens of theoretical computer science, verifying the correctness of a mathematical proof is a fundamental computational task. Indeed, the P versus NP problem, which deals precisely with the complexity of proof verification, is one of the most important open problems in all of mathematics.

    The complexity-theoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit local-to-global structure that allows verifying a proof by reading only a minuscule portion of it. As another example, interactive proofs allow for verification via a conversation between a prover and a verifier, instead of the traditional static sequence of logical statements. The study of such proof systems has drawn upon deep mathematical tools to derive numerous applications to the theory of computation and beyond.

    In recent years, such probabilistic proofs received much attention due to a new motivation, delegation of computation, which is the emphasis of this summer school. This paradigm admits ultra-fast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recently-deployed technology, for example, as part of cryptographic constructions known as succinct non-interactive arguments of knowledge (SNARKs).

    This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.

    Updated on Feb 11, 2021 01:48 PM PST
  27. 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 California, San Diego), Alice Guionnet (École Normale Supérieure de Lyon), Alexander Its (Indiana University-Purdue University Indianapolis), Herbert Spohn (Technische Universität München), Horng-Tzer Yau (Harvard University)
    Image

    The past decade has seen tremendous progress in understanding the behavior of large random matrices and interacting particle systems. Complementary methods have emerged to prove universality of these behaviors, as well as to probe their precise nature using integrable, or exactly solvable models. This program seeks to reinforce and expand the fruitful interaction at the interface of these areas, as well as to showcase some of the important developments and applications of the past decade.

    Updated on Apr 20, 2020 11:12 AM PDT
  28. Program Complementary Program 2021-22

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program.

    Updated on Jan 15, 2021 11:53 AM PST
  29. Workshop Connections Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems

    Organizers: LEAD Ioana Dumitriu (University of California, San Diego), Alisa Knizel (The University of Chicago)
    Image
    An illustration of the TASEP interface growth by Leonid Petrov and Hao Yu Li.

    This workshop will focus on cutting-edge research in random matrices and integrable probability. We will 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. 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 May 06, 2020 11:42 AM PDT
  30. Workshop Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems

    Organizers: LEAD Gerard Ben Arous (New York University, Courant Institute), Alice Guionnet (École Normale Supérieure de Lyon), Sylvia Serfaty (New York University, Courant Institute), Horng-Tzer Yau (Harvard University)

    The introductory 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 Mar 19, 2020 11:30 AM PDT
  31. Workshop 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), Lu Wang (California Institute of Technology)
    Adriaen hanneman two boys blowing bubbles

    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 Dec 04, 2020 01:14 PM PST
  32. 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; International School for Advanced Studies (SISSA/ISAS)), Alexander Its (Indiana University-Purdue University Indianapolis), Sandrine Péché (Université de Paris VII (Denis Diderot))
    Image
    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
  33. 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), Jang-Mei Wu (University of Illinois at Urbana-Champaign)
    Graphisc

    This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers,  random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

    Updated on Nov 20, 2019 02:12 PM PST
  34. 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 (Université d'Aix-Marseille (AMU)), Mitsuhiro Shishikura (Kyoto University), Dylan Thurston (Indiana University)
    Image
    The mating of these two dendritic Julia sets is equal to the Julia set of a rational map of degree 2; that Julia set is equal to the entire Riemann sphere. Picture by Arnaud Chéritat

    Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond. 

    Our semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. We will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics. 

    Updated on Nov 20, 2019 02:12 PM PST
  35. Workshop 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)
    Image3
    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
  36. Workshop 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 Indianapolis), Dierk Schleicher (Université d'Aix-Marseille (AMU)), Mitsuhiro Shishikura (Kyoto University)
    Image
    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
  37. Program Floer Homotopy Theory

    Organizers: Mohammed Abouzaid (Columbia University), Andrew Blumberg (University of Texas, Austin), Kristen Hendricks (Rutgers University), Robert Lipshitz (University of Oregon), LEAD Ciprian Manolescu (Stanford University), Nathalie Wahl (University of Copenhagen)
    335 image
    Illustrated by Nathalie Wahl

    The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes.  In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and low-dimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory. 

    Updated on Oct 02, 2020 03:01 PM PDT
  38. Program Analytic and Geometric Aspects of Gauge Theory

    Organizers: Laura Fredrickson (University of Oregon), Rafe Mazzeo (Stanford University), Tomasz Mrowka (Massachusetts Institute of Technology), Laura Schaposnik (University of Illinois at Chicago), LEAD Thomas Walpuski (Humboldt-Universität)
    Gt 2022 23 fall image.2019.01.07. orig   fixed999

    The mathematics and physics around gauge theory have, since their first interaction in the mid 1970’s, prompted tremendous developments in both mathematics and physics.  Deep and fundamental tools in partial differential equations have been developed to provide rigorous foundations for the mathematical study of gauge theories.  This led to ongoing revolutions in the understanding of manifolds of dimensions 3 and 4 and presaged the development of symplectic topology.  Ideas from quantum field theory have provided deep insights into new directions and conjectures on the structure of gauge theories and suggested many potential applications.  The focus of this program will be those parts of gauge theory which hold promise for new applications to geometry and topology and require development of new analytic tools for their study.

    Updated on Oct 28, 2020 09:12 AM PDT
  39. Program Algebraic Cycles, L-Values, and Euler Systems

    Organizers: Henri Darmon (McGill University), Ellen Eischen (University of Oregon), LEAD Benjamin Howard (Boston College), David Loeffler (University of Warwick), Christopher Skinner (Princeton University), Sarah Zerbes (University College London), Wei Zhang (Massachusetts Institute of Technology)
    Image
    Some Gaussian periods for the 255,255-th cyclotomic extension. Image credit: E. Eischen, based on earlier work by W. Duke, S. R. Garcia, T. Hyde, and R. Lutz

    The fundamental conjecture of Birch and Swinnerton-Dyer relating the Mordell–Weil ranks of elliptic curves to their L-functions is one of the most important and motivating problems in number theory. It resides at the heart of a collection of important conjectures (due especially to Deligne, Beilinson, Bloch and Kato) that connect values of L-functions and their leading terms to cycles and Galois cohomology groups. 

    The study of special algebraic cycles on Shimura varieties has led to progress in our understanding of these conjectures. The arithmetic intersection numbers and the p-adic regulators of special cycles are directly related to the values and derivatives of L-functions, as shown in the pioneering theorem of Gross-Zagier and its p-adic avatars for Heegner points on modular curves. The cohomology classes of special cycles (and related constructions such as Eisenstein classes) form the foundation of the theory of Euler systems, providing one of the most powerful methods known to prove vanishing or finiteness results for Selmer groups of Galois representations. 

    The goal of this semester is to bring together researchers working on different aspects of this young but fast-developing subject, and to make progress on understanding the mysterious relations between L-functions, Euler systems, and algebraic cycles.

    Updated on Feb 25, 2020 11:41 AM PST
  40. Program Diophantine Geometry

    Organizers: Jennifer Balakrishnan (Boston University), Mirela Ciperiani (University of Texas, Austin), Philipp Habegger (University of Basel), Wei Ho (University of Michigan), LEAD Hector Pasten (Pontificia Universidad Católica de Chile), Yunqing Tang (Université Paris-Sud), Shou-Wu Zhang (Princeton University)
    Image
    A rational point on a curve of genus 3

    While the study of rational solutions of diophantine equations initiated thousands of years ago, our knowledge on this subject has dramatically improved in recent years. Especially, we have witnessed spectacular progress in aspects such as height formulas and height bounds for algebraic points, automorphic methods, unlikely intersection problems, and non-abelian and p-adic approaches to algebraic degeneracy of rational points. All these groundbreaking advances in the study of rational and algebraic points in varieties will be the central theme of the semester program “Diophantine Geometry” at MSRI. The main purpose of this program is to bring together experts as well as enthusiastic young researchers to learn from each other, to initiate and continue collaborations, to update on recent breakthroughs, and to further advance the field by making progress on fundamental open problems and by developing further connections with other branches of mathematics. We trust that younger mathematicians will greatly contribute to the success of the program with their new ideas. It is our hope that this program will provide a unique opportunity for women and underrepresented groups to make outstanding contributions to the field, and we strongly encourage their participation.

    Updated on Feb 25, 2021 04:59 PM PST