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Upcoming Summer Graduate Schools

  1. Commutative Algebra and its Interaction with Algebraic Geometry (Notre Dame)

    Organizers: Steven Cutkosky (University of Missouri), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame), Steven Sam (University of California, San Diego), Kevin Tucker (University of Illinois at Chicago)
    1015 image

    Commutative Algebra has seen an extraordinary development in the last few years. Long standing conjectures have been proven and new connections to different areas of mathematics have been built.This summer graduate school will consist of three mini-courses (5 lectures each) on fundamental topics in commutative algebra that are not covered in the standard courses. Each course will be accompanied by problem sessions focused on research. Five general colloquium-style lectures will be given by invited scholars who will also attend the school and help with afternoon research activities. 

    Updated on Sep 26, 2022 12:06 PM PDT
  2. Formalization of Mathematics

    Organizers: Jeremy Avigad (Carnegie Mellon University), Heather Macbeth (Fordham University at Lincoln Center), Patrick Massot (Université Paris-Saclay)
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    Some basic concepts in mathlib and the dependencies between them

    Computational proof assistants now make it possible to develop global, digital mathematical libraries with theorems that are fully checked by computer. This summer school will introduce students to the new technology and the ideas behind it, and will encourage them to think about the goals and benefits of formalized mathematics. Students will learn to use the Lean interactive proof assistant, and by the end of the session they will be in a position to formalize mathematics on their own, join the Lean community, and contribute to its mathematical library.

    Updated on Sep 26, 2022 09:18 AM PDT
  3. Machine Learning (UCSD)

    Organizers: Ery Arias-Castro, Mikhail Belkin (University of California, San Diego), Yusu Wang (Univ. California, San Diego), Lily Weng (University of California, San Diego)

    The overarching goal of this summer school is to expose the students both to modern forms of unsupervised learning — in the form of geometrical and topological data analysis — and to supervised learning — in the form of (deep) neural networks applied to regression/classification problems. The organizers have opted for a lighter exposure to a broader range of topics. Using the metaphor of a meal, we are offering 2 + 2 samplers — geometry and topology for data analysis + theoretical and practical deep learning — rather than 1 + 1 main dishes. The main goal, thus, is to inspire the students to learn more about one or several of the topics covered in the school.

    The expected learning outcomes for students attending the school are the following:

    1. An introduction to how concepts and tools from geometry and topology can be leveraged to perform data analysis in situations where the data are not labeled.

    2. An introduction to recent and ongoing theoretical and methodological/practical developments in the use of neural networks for data analysis (deep learning).

    Updated on Sep 26, 2022 02:47 PM PDT
  4. Algebraic Methods for Biochemical Reaction Networks (Leipzig, Germany)

    Organizers: Timo de Wolff (TU Berlin), LEAD Alicia Dickenstein (University of Buenos Aires), Elisenda Feliu (University of Copenhagen)
    2021 sgs biochemical reaction networks leipzig image dickenstein.2019.10.09 %281%29
    A basic enzymatic mechanism

    The aim of the course is to learn how tools from algebraic geometry (in particular, from computational and real algebraic geometry) can be used to analyze standard models in molecular biology. Particularly, these models are key ingredients in the development of Systems and Synthetic biology, two active research areas focusing on understanding, modifying, and implementing the design principles of living systems.

    We will focus on the mathematical aspects of the methods, and exemplify and apply the theory to real networks, thereby introducing the participants to relevant problems and mechanisms in molecular biology. As a counterpart, however, the participants will also see how this field has in the past challenged current methods, mainly in the realm of real algebraic geometry, and has given rise to new general and purely theoretical results on polynomial equations. We will end our lectures with an overview of open questions in both fields.

    Updated on Sep 28, 2022 08:50 AM PDT
  5. Séminaire de Mathématiques Supérieures 2023: Periodic and Ergodic Spectral Problems

    Organizers: David Damanik (Rice University), Alexander Elgart (Virginia Polytechnic Institute and State University), Vojkan Jaksic (McGill University), Svetlana Jitomirskaya (University of California, Irvine), Jean Lagacé (University College London), Iosif Polterovich (Université de Montréal)

    This two week school will focus on spectral theory of periodic, almost-periodic, and random operators.  The main aim of this school is to teach the students who work in one of these areas, methods used in parallel problems, explain the similarities between all these areas and show them the `big picture'.

    Updated on Sep 26, 2022 01:54 PM PDT
  6. Mathematics and Computer Science of Market and Mechanism Design

    Organizers: Yannai Gonczarowski (Microsoft Research), Irene Yuan Lo (Stanford University), Ran Shorrer (Pennsylvania State University), LEAD Inbal Talgam-Cohen (Technion---Israel Institute of Technology)

    This school is associated with an upcoming research program at MSRI under the same title. The goal of the school is to equip students unfamiliar with these topics with the mathematical and theoretical computer science toolbox that forms the foundation of market and mechanism design.

    Updated on Sep 23, 2022 05:05 PM PDT
  7. Topics in Geometric Flows and Minimal Surfaces

    Organizers: Ailana Fraser (University of British Columbia), Lan-Hsuan Huang (University of Connecticut), Catherine Searle (Wichita State University), Lu Wang (Yale University)
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    Soap bubble: equilibrium solution of the rescaled mean curvature flow and constant curvature surface.

    This graduate summer school will introduce students to two important and inter-related fields of differential geometry: geometric flows and minimal surfaces.

    Geometric flows have had far reaching influences on numerous branches of mathematics and other scientific disciplines. An outstanding example is the completion of Hamilton’s Ricci flow program by Perelman, leading to the resolution of the Poincare conjecture and Thurston’s geometrization conjecture for 3-manifolds. In this part of the summer school, students will be guided through basic topics and ideas in the study of geometric flows.

    Since Penrose used variations of volume to formulate and study black holes in general relativity (in his Nobel prize-winning work), the intriguing connections between minimal surfaces and general relativity have been a strong driving force for the modern developments of both research areas. This part of the summer school will introduce students to the basic theory of minimal submanifolds and its applications in Riemannian geometry and general relativity.

    The curriculum of this program will be accessible and will have a broad appeal to graduate students from a variety of mathematical areas, introducing some of the latest developments in each area and the remaining open problems therein, while simultaneously emphasizing their synergy.

    Updated on Sep 26, 2022 12:27 PM PDT
  8. Introduction to Derived Algebraic Geometry

    Organizers: Benjamin Antieau (Northwestern University), Dmytro Arinkin (University of Wisconsin-Madison)
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    Schur quartic x 4−xy3 = z 4−zu3 and several of the 64 lines that it contains

    Derived algebraic geometry is an ‘update’ of algebraic geometry using ‘derived’ (roughly speaking, homological) techniques. This requires recasting the very foundations of the field: rings have to be replaced by differential graded algebras (or other forms of derived rings), categories by higher categories, and so on. The result is a powerful set of new tools, useful both within algebraic geometry and in related areas. The school serves as an introduction to these techniques, focusing on their applications.

    The school is built around two related courses on geometric (‘derived spaces’) and categorical (‘derived categories’) aspects of the theory. Our goal is to explain the key ideas and concepts, while trying to keep technicalities to a minimum.

    Updated on Sep 28, 2022 05:43 PM PDT