
Summer Graduate School Mathematics of Big Data: Sketching and (Multi) Linear Algebra (Virtual School)
Organizers: LEAD Kenneth Clarkson (IBM Research Division), Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University), Tamara Kolda (Sandia National Laboratories), Shashanka Ubaru (IBM Thomas J. Watson Research Center)This summer school will introduce graduate students to sketchingbased approaches to computational linear and multilinear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.
Updated on Mar 15, 2021 03:16 PM PDT 
Summer Graduate School Gauge Theory in Geometry and Topology (Virtual School)
Organizers: Lynn Heller (Universität Hannover), Francesco Lin (Columbia University), LEAD Laura Starkston (University of California, Davis), Boyu Zhang (Princeton University)Figure 1. A rotationally symmetric solution to the selfduality equations on an open and dense subset of the torus. Singularities appear where the surface intersects the ideal boundary at infinity of the hyperbolic 3space 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 lowdimensional 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 lowdimensional topology. By the end of the twoweek program, the students will understand the relevant analytic and geometric aspects of several partial differential equations of current interest (including the YangMills ASD equations, the SeibergWitten equations, and the Hitchin equations) and some of their most impactful applications to problems in geometry and topology.
Updated on Jun 10, 2021 09:28 AM PDT 
Summer Graduate School Random Conformal Geometry (Virtual School)
Organizers: Mario Bonk (University of California, Los Angeles), Steffen Rohde (University of Washington), LEAD Fredrik Viklund (Royal Institute of Technology)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 semesterlong program "The Analysis and Geometry of Random Spaces". Specific topics are Conformal Field Theory, Brownian Loops and related processes, Quasiconformal Maps, as well as Loewner Energy and Teichmüller Theory.
Updated on Mar 19, 2021 03:03 PM PDT 
Summer Graduate School Foundations and Frontiers of Probabilistic Proofs (Virtual School)
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 Apr 19, 2021 06:23 PM PDT 
Workshop Blackwell Tapia Conference 2021
Organizers: David Banks (Duke University), Hélène Barcelo (MSRI  Mathematical Sciences Research Institute), Lloyd Douglas, Robert Megginson (University of Michigan), Mariel Vazquez (University of California, Davis), Ulrica Wilson (Morehouse College; Institute for Computational and Experimental Research in Mathematics (ICERM))The 2020 BlackwellTapia Conference has been rescheduled to 2021. The Prize Winner is Tatiana Toro, Professor of Mathematics, University of Washington.
Description: Held every other year, the conference and prize honor David Blackwell, the first AfricanAmerican member of the National Academy of Science, and Richard Tapia, winner of the National Medal of Science in 2010, two seminal figures who inspired a generation of AfricanAmerican, Native American, and Latino/Latina students to pursue careers in mathematics. The BlackwellTapia Prize recognizes a mathematician who has contributed significantly to research in his or her area of expertise, and who has served as a role model for mathematical scientists and students from underrepresented minority groups or has contributed in other significant ways to addressing the problem of underrepresentation of minorities in math.
Updated on Jun 02, 2021 11:33 AM PDT

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