Home » Articles posted by Alenia Reynoso Added on November 13, 2023 by Alenia ReynosoTitle: Dieudonné theory: from classical to modern
Abstract: Dieudonné theory gives a classification in terms of “semilinear algebra” of finite flat commutative group schemes of ppower order over a perfect field of characteristic p > 0. Over the years, Dieudonné theory has evolved in many forms (crystalline, prismatic) and recently V. Drinfeld has proposed various “Shimurian” generalizations of the theory. I will give an introduction to and overview of some of this history and more recent developments.
Print this pageAdded on November 13, 2023 by Alenia ReynosoTitle: Fourier uniformity of multiplicative functions
Abstract: The Fourier uniformity conjecture seeks tounderstand what multiplicative functions can have large Fourier coefficients onmany short intervals. We will discuss recent progress on this problem andexplain its connection with the distribution of prime numbers and with othercentral problems about the behaviour of multiplicative functions, such as theChowla and Sarnak conjectures.
Print this pageAdded on October 12, 2023 by Alenia ReynosoSpeaker: Maryna Viazovska (EPFL)
Title: Random lattices with symmetries
Abstract: What is the densest lattice sphere packing in the ddimensional Euclidean space? In this talk, we will investigate this question as the dimension goes to infinity, and we will focus on the lower bounds for the best packing density, or in other words, on the existence results. We will give a historical overview of the lower bounds proved by H. Minkowski, E. Hlawka, C. L. Siegel, C. A. Rogers, and more recently by S. Vance and A. Venkatesh. In the final part of the lecture, we will present recent work done in collaboration with V. Serban and N. Gargava on the moments of the number of lattice points in a bounded set for random lattices constructed from a number field.
Mathematics Hall, room 417 from 4:30 – 5:30pm
Print this pageAdded on September 26, 2023 by Alenia ReynosoSpeaker: Professor Ezra Getzler (Northwestern University)
Title: Generalizing Lie theory to higher dimensions – the De Rham theorem on simplices and cubes
Abstract: There is a generalization of Lie theory from Lie algebras to differential graded Lie algebras. Ordinary Lie theory involves first order ordinary differential equations. Higher Lie theory may be understood as a nonlinear generalization of the de Rham theorem on simplicial complexes (in Dupont’s formulation), as against graphs. In this talk, we present an alternate approach to this theory, using the more elementary de Rham theorem on cubical complexes.
Along the way, we will need an interesting relationship between cubical and simplicial complexes, which has recently become better known due to its use in Lurie’s theory of straightening for infinity categories.
Mathematics Hall, room 407 from 4:30 – 5:30pm
Print this pageAdded on September 21, 2023 by Alenia ReynosoThe Graduate School of Arts and Sciences joins the greater Columbia community in mourning the loss of Henry Pinkham, former dean, chair, and professor for nearly 50 years, who passed away suddenly in late June 2023.
A memorial service for Professor Pinkham is planned for Friday, November 17, 2023, from 11:00 am – 2:00 pm at Faculty House.
RSVPs should be sent to sophie.pinkham@gmail.com.
For more information, please visit: https://www.gsas.columbia.edu/content/memoriamhenrycpinkhamformerdeangsas
Print this pageAdded on September 14, 2023 by Alenia ReynosoSpecial Lecture Series
Speaker: Professor Nikita Nekrasov (Simons Center for Geometry and Physics and Columbia)
The Count of Instatons
Abstract: Graduate level introduction to modern mathematical physics with the emphasis on the geometry and physics of quantum gauge theory and its connections to string theory. We shall zoom in on a corner of the theory especially suitable for exploring nonperturbative aspects of gauge and string theory: the instanton contributions. Using a combination of methods from algebraic geometry, topology, representation theory and probability theory we shall derive a series of identities obeyed by generating functions of integrals over instanton moduli spaces, and discuss their symplectic, quantum, isomonodromic, and, more generally, representationtheoretic significance.
Quantum and classical integrable systems, both finite and infinitedimensional ones, will be a recurring cast of characters, along with the other (qq) characters.
First lecture: Friday, September 15, 2023
Fridays at 1:30pm until 3pm (except for the following dates: 10/6 , 10/20/, 11/3, 11/17, 11/24, 12/112/8 (TBD), and 12/15)
Room 520, Mathematics Hall
2990 Broadway (117th Street)
Flyer
Notes
Lecture notes: Not split per lecture will be updated as course continues
Lecture recording
Print this pageAdded on September 14, 2023 by Alenia ReynosoSimon Brendle, a professor of mathematics, has been awarded the Breakthrough Prize. The annual prize was founded in 2012 by sponsors Sergey Brin, Priscilla Chan and Mark Zuckerberg, Julia and Yuri Milner, and Anne Wojcicki, and touts itself as the world’s largest international science prize. It comes with a $3 million award. Professor Brendle was recognized for “a series of remarkable leaps in differential geometry, a field that uses the tools of calculus to study curves, surfaces and spaces. Many of his results concern the shape of surfaces, as well as manifolds in higher dimensions than those we experience in everyday life.”
“We’re thrilled to see Professor Brendle’s work recognized in such a public way. His ongoing research on differential geometry and nonlinear partial differential equations is of vital importance for the field, and he is a treasured member of the Columbia community,” said Johan de Jong, the chair of the mathematics department.
For more information, please visit Professor Simon Brendle Wins Breakthrough Prize  Columbia News
Columbia’s Instagram post
Breakthrough Reception 2023 photos by Eileen Barroso for Columbia Research Teams
Photo credits: Photographer Eileen Barroso
Print this pageAdded on August 21, 2023 by Alenia ReynosoThe Fall 2023 Minerva Foundation Lectures will take place on Wednesdays at 2:45 p.m. in room 507. Professor Sergiu Klainerman (Princeton University), will deliver a series of lectures titled:
Columbia Lectures on the Stability of Kerr
The main goals of these lectures are:
1. Provide a comprehensive introduction to the proof of the nonlinear stability of slowly rotating Kerr black holes established recently in the sequence of works [KlSz:Kerr], [GKS2022], [KlSz:GCM1], [KlSz:GCM2] and [Shen], and briefed in [KlSz:review].
2. Discuss the geometric formalism based on nonintegrable null horizontal structures used in these works. Derive the main Teukolsky and generalized Regge Wheeler equations. These follow the material 1 of Part 1 in [GKS2022].
3. Discuss the proof of the basic hyperbolic estimates, Morawetz and rpweighted, following Part 2 of [GKS2022].
4. Discuss open problems related to these topics.
First lecture: Wednesday, September 6, 2023
Meeting on Wednesdays at 2:45 p.m.
Room 507, Mathematics Hall
2990 Broadway (117th Street)
Flyer
Notes
Notes Part II
Notes Part III
Lecture recording
Print this pageAdded on August 18, 2023 by Alenia ReynosoThe Fall 2023 Samuel Eilenberg Lectures will take place on Tuesdays at 4:10 p.m. in room 520. Professor Laurent Fargues (Institut de Mathématiques de JussieuParis), will deliver a series of lectures titled:
Some new geometric structures in the Langlands program
Abstract: Starting from HarrisTaylor and my PHD work on the geometric realization of the local Langlands correspondences to my recent joint work with Scholze, I will explain the new geometric structures that have emerged in the Langlands program. For the first time, ideas of the geometric Langlands program have been imported into the classical Langlands program in characteristic zero. To give life to those ideas we developed with Scholze some new geometry, following my work with Fontaine where we began to give a meaning to the idea of an holomorphic function of the variable p where p is a prime number. I will explain this new geometry and its applications to the Langlands program.”
First lecture: Tuesday, September 12, 2023
Tuesdays at 4:10pm
Room 520, Mathematics Hall
2990 Broadway (117th Street)
Flyer
Notes
Lecture recording
Print this pageAdded on May 15, 2023 by Alenia ReynosoCOMAP is pleased to announce the results of the 39th annual Mathematical Contest in Modeling (MCM). This year, 11,296 teams representing institutions from twentyone countries/regions participated in the contest. TwentyTwo teams from the following institutions were designated as OUTSTANDING WINNERS.
The first team consisting of Maksym Bondarenko, Philip M. Yan, and Caden Lin, received the title of Outstanding Winner and was awarded the MAA award.
To view the seven outstanding winners of the MCM (A) Problem, please visit this link.
The second team consisting of Steven Sofos DiSilvio, Anthony Ozerov, and Leon Zhou, received the title of Outstanding Winner and was awarded the INFORMS and the MAA award.
To view the twelve outstanding winner of the MCM (C) Problem, please visit this link.
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