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 All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.   All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. 
   
−  ==Spring 2019==
 
   
 +  
 +  ==Fall 2019== 
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−  Jan 25 '''Room 911'''  +  Sept 6 
−   [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW
 
−  [[#Beata Randrianantoanina (Miami University Ohio)  Some nonlinear problems in the geometry of Banach spaces and their applications ]]
 
−   Tullia Dymarz
 
     
−  
 
−  Jan 30 '''Wednesday'''
 
−   Talk rescheduled to Feb 15
 
     
     
−  Jan 31 '''Thursday'''  +  Sept 13 
−   Talk rescheduled to Feb 13  +   Jan Soibelman (Kansas State) 
 +  [[# TBA TBA ]] 
 +   Caldararu 
     
     
−  Feb 1  +  Sept 16 '''Monday Room 911''' 
−   Talk cancelled due to weather  +   Alicia Dickenstein (Buenos Aires) 
−    +  [[# TBA TBA ]] 
−    +   Craciun 
     
     
−  Feb 5 '''Tuesday, VV 911'''  +  Sept 20 
−   [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University)  +   Jianfeng Lu (Duke) 
−  [[#Alexei Poltoratski (Texas A&M) Completeness of exponentials: BeurlingMalliavin and type problems ]]  +  [[#TBA  TBA]] 
−   Denisov  +   Qin 
     
     
−  Feb 6 '''Wednesday, room 911'''  +  Sept 27 
−   [https://lctsai.github.io/ LiCheng Tsai] (Columbia University)  +  Elchnanan Mossel (MIT) Distinguished Lecture 
−  [[#LiCheng Tsai (Columbia University) When particle systems meet PDEs ]]
 
−   Anderson
 
−  
 
     
−  Feb 8  +  Oct 4 
−   [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)  +   Matt Baker (Georgia Tech) 
−  [[#Aaron Naber (Northwestern)  A structure theory for spaces with lower Ricci curvature bounds ]]
 
−   Street
 
     
     
−  Feb 11 '''Monday'''  +  Oct 11 
−   [https://www2.bc.edu/davidtreumann/materials.html David Treumann] (Boston College)
 
−  [[#David Treumann (Boston College)  Twisting things in topology and symplectic topology by pth powers ]]
 
−   Caldararu
 
     
     
−   Feb 13 '''Wednesday'''  +  Oct 18 
−   [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M)
 
−  [[#Dean Baskin (Texas A&M)  Radiation fields for wave equations ]]
 
−   Street
 
−   
−  
 
−   Feb 15
 
−   [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University)
 
−   [[#Lillian Pierce (Duke University)  Short character sums ]]
 
−   Boston and Street
 
     
     
−  Feb 22  +  Oct 25 
−   [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)
 
−  [[#Angelica Cueto (The Ohio State University) Lines on cubic surfaces in the tropics ]]
 
−   Erman and Corey
 
     
     
−  March 4 '''Monday'''  +  Nov 1 
−   [http://wwwusers.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota)  +  Possibly reserved for job talk? 
−  [[#Vladimir Sverak (Minnesota)  Wasow lecture "PDE aspects of the NavierStokes equations and simpler models" ]]
 
−   Kim
 
     
     
−  March 8  +  Nov 8 
−   [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)  +  Reserved for job talk 
−  [[#Jason McCullough (Iowa State) On the degrees and complexity of algebraic varieties ]]
 
−   Erman
 
     
     
−  March 15  +  Nov 15 
−   <s>[http://www.its.caltech.edu/~maksym/ Maksym Radziwill] (Caltech)</s> <b>Talk cancelled</b>  +  Reserved for job talk 
−  [[#Maksym Radziwill (Caltech)  <s>Recent progress in multiplicative number theory</s> ]]
 
−   Marshall
 
     
     
−  March 29  +  Nov 22 
−   Jennifer Park (OSU)  +  Reserved for job talk 
−  [[#Jennifer Park (OSU)  Rational points on varieties ]]
 
−   Marshall
 
     
     
−  April 5  +  Nov 29 
−   JuLee Kim (MIT)  +  Thanksgiving 
−  [[#JuLee Kim (MIT)  Types and counting automorphic forms ]]
 
−   Gurevich
 
     
     
−  April 12  +  Dec 6 
−   Eviatar Procaccia (TAMU)  +  Reserved for job talk 
−  [[#Eviatar Procaccia  Can one hear the shape of a random walk? ]]
 
−   Gurevich
 
     
     
−  April 19  +  Dec 13 
−   [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)  +  Reserved for job talk 
−  [[#Jo Nelson (Rice) Contact Invariants and Reeb Dynamics ]]
 
−   JeanLuc
 
−  
 
−  
 
−  April 22 '''Monday'''
 
−   [https://justinh.su Justin Hsu] (Madison)
 
−  [[#Justin Hsu (Madison)  From Couplings to Probabilistic Relational Program Logics ]]
 
−   Lempp
 
−  
 
−  
 
−  April 26 '''Room 911'''
 
−   [https://www.brown.edu/academics/appliedmathematics/faculty/kavitaramanan/home Kavita Ramanan] (Brown University)
 
−  [[# Kavita Ramanan (Brown)  Tales of Random Projections ]]
 
−   WIMAW
 
−  
 
−  
 
−  May 3
 
−   Tomasz Przebinda (Oklahoma)
 
−  [[# TBA TBA ]]
 
−   Gurevich
 
     
 }   } 
   
 +  ==Spring 2020== 
   
− 
 
− 
 
− 
 
− 
 
−  ==FALL 2019==
 
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 +   
     
−  Sept 6  +  Jan 24 
     
 +   
 +  Jan 31 
     
     
−  Sept 13  +  Feb 7 
−   Jan Soibelman (Kansas State)
 
−  [[# TBA TBA ]]
 
−   Caldararu
 
     
     
−  Sept 16 '''Monday Room 911'''  +  Feb 14 
−   Alicia Dickenstein (Buenos Aires)
 
−  [[# TBA TBA ]]
 
−   Craciun
 
     
     
−  Sept 20  +  Feb 21 
     
     
−  Sept 27  +  Feb 28 
     
     
−  Oct 4  +  March 6 
     
     
−  Oct 11  +  March 13 
     
     
−  Oct 18  +  March 20 
 +  Spring break 
     
     
−  Oct 25  +  March 27 
     
     
−  Nov 1  +  April 3 
     
     
−  Nov 8  +  April 10 
 +   Sarah Koch (Michigan) 
     
 +   Bruce (WIMAW) 
     
−  Nov 15  +  April 17 
     
     
−  Nov 22  +  April 24 
     
     
−  Nov 29 '''Thanksgiving'''  +  May 1 
−    +  Robert Lazarsfeld (Stony Brook) 
 +  Distinguished lecture 
 +  Erman 
 }   } 
− 
 
− 
 
   
 == Abstracts ==   == Abstracts == 
   
−  ===Beata Randrianantoanina (Miami University Ohio)===  +  ===Person (Institution)=== 
−   
−  Title: Some nonlinear problems in the geometry of Banach spaces and their applications.
 
−   
−  Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.
 
−   
−  ===Lillian Pierce (Duke University)===
 
   
−  Title: Short character sums  +  Title: 
   
−  Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a socalled character sum. For example, both understanding the Riemann zeta function or Dirichlet Lfunctions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.  +  Abstract: 
−   
−  ===Angelica Cueto (The Ohio State University)===
 
−  Title: Lines on cubic surfaces in the tropics
 
−   
−  Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The wellknow statement <i>any smooth surface of degree three in P^3 contains exactly 27 lines</i> is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.
 
−   
−  In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.
 
−   
−  ===David Treumann (Boston College)===
 
−   
−  Title: Twisting things in topology and symplectic topology by pth powers
 
−   
−  Abstract: There's an old and popular analogy between circles and finite fields. I'll describe some constructions you can make in Lagrangian Floer theory and in microlocal sheaf theory by taking this analogy extremely literally, the main ingredient is an "Ffield." An Ffield on a manifold M is a local system of algebraically closed fields of characteristic p. When M is symplectic, maybe an Ffield should remind you of a Bfield, it can be used to change the Fukaya category in about the same way. On M = S^1 times R^3, this version of the Fukaya category is related to DeligneLusztig theory, and I found something like a cluster structure on the DeligneLusztig pairing varieties by studying it. On M = S^1 times S^1, Yanki Lekili and I have found that this version of the Fukaya category is related to the equalcharacteristic version of the FarguesFontaine curve; the relationship is homological mirror symmetry.
 
−   
−  ===Dean Baskin (Texas A&M)===
 
−   
−  Title: Radiation fields for wave equations
 
−   
−  Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.
 
−   
−  ===Jianfeng Lu (Duke University)===
 
−   
−  Title: Density fitting: Analysis, algorithm and applications
 
−   
−  Abstract: Density fitting considers the lowrank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the lowrank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.
 
−   
−  ===Alexei Poltoratski (Texas A&M)===
 
−   
−  Title: Completeness of exponentials: BeurlingMalliavin and type problems
 
−   
−  Abstract: This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both
 
−  problems ask when a family of complex exponentials is complete (spans) an L^2space. The BerulingMalliavin
 
−  problem was solved in the early 1960s and I will present its classical solution along with modern generalizations
 
−  and applications. I will then discuss history and recent progress in the type problem, which stood open for
 
−  more than 70 years.
 
−   
−  ===LiCheng Tsai (Columbia University)===
 
−   
−  Title: When particle systems meet PDEs
 
−   
−  Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing realworld phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems.
 
−   
−  ===Aaron Naber (Northwestern)===
 
−   
−  Title: A structure theory for spaces with lower Ricci curvature bounds.
 
−   
−  Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.
 
−   
−   
−  ===Vladimir Sverak (Minnesota)===
 
−   
−  Title: PDE aspects of the NavierStokes equations and simpler models
 
−   
−  Abstract: Does the NavierStokes equation give a reasonably complete description of fluid motion? There seems to be no empirical evidence which would suggest a negative answer (in regimes which are not extreme), but from the purely mathematical point of view, the answer may not be so clear. In the lecture, I will discuss some of the possible scenarios and open problems for both the full equations and simplified models.
 
−   
−   
−  ===Jason McCullough (Iowa State)===
 
−   
−  Title: On the degrees and complexity of algebraic varieties
 
−   
−  Abstract: Given a system of polynomial equations in several variables, there are several natural questions regarding its associated solution set (algebraic variety): What is its dimension? Is it smooth or are there singularities? How is it embedded in affine/projective space? Free resolutions encode answers to all of these questions and are computable with modern computer algebra programs. This begs the question: can one bound the computational complexity of a variety in terms of readily available data? I will discuss two recently solved conjectures of Stillman and EisenbudGoto, how they relate to each other, and what they say about the complexity of algebraic varieties.
 
−   
−  ===Maksym Radziwill (Caltech)===
 
−   
−  Title: Recent progress in multiplicative number theory
 
−   
−  Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (such as primes). It is a central area of analytic number theory with various connections to Lfunctions, harmonic analysis, combinatorics, probability etc. At the core of the subject lie difficult questions such as the Riemann Hypothesis, and they set a benchmark for its accomplishments.
 
−  An outstanding challenge in this field is to understand the multiplicative properties of integers linked by additive conditions, for instance n and n+ 1. A central conjecture making this precise is the ChowlaElliott conjecture on correlations of multiplicative functions evaluated at consecutive integers. Until recently this conjecture appeared completely out of reach and was thought to be at least as difficult as showing the existence of infinitely many twin primes. These are also the kind of questions that lie beyond the capability of the Riemann Hypothesis. However recently the landscape of multiplicative number theory has been changing and we are no longer so certain about the limitations of our (new) tools. I will discuss the recent progress on these questions.
 
−   
−  ===Jennifer Park (OSU)===
 
−   
−  Title: Rational points on varieties
 
−   
−  Abstract: The question of finding rational solutions to systems of polynomial equations has been investigated at least since the days of Pythagoras, but it is still not completely resolved (and in fact, it has been proven that there will never be an algorithm that answers this question!) Nonetheless, we will discuss various techniques that could answer this question in certain cases, and we will outline some conjectures related to this problem as well.
 
−   
−  ===JuLee Kim (MIT)===
 
−   
−  Title: Types and counting automorphic forms
 
−   
−  Abstract: We review the theory of types in representations of padic groups and discuss some applications for quantifying automorphic forms.
 
−   
−  ===Eviatar Procaccia===
 
−   
−  Title: Can one hear the shape of a random walk?
 
−   
−  Abstract: We consider a Gibbs distribution over random walk paths on the square lattice, proportional to a random weight of the path’s boundary . We show that in the zero temperature limit, the paths condensate around an asymptotic shape. This limit shape is characterized as the minimizer of the functional, mapping open connected subsets of the plane to the sum of their principle eigenvalue and perimeter (with respect to the first passage percolation norm). A prime novel feature of this limit shape is that it is not in the class of Wulff shapes.
 
−  Joint work with Marek Biskup (UCLA)
 
−   
−  ===Jo Nelson (Rice)===
 
−   
−  Title: Contact Invariants and Reeb Dynamics
 
−   
−  Abstract: Contact geometry is the study of certain geometric structures on odd dimensional smooth manifolds. A contactstructure is a hyperplane field specified by a one form which satisfies a maximum nondegeneracy condition called complete nonintegrability. The associated one form is called a contact form and uniquely determines a vector field called the Reeb vector field on the manifold. I will explain how to make use of Jholomorphic curves to obtain a Floer theoretic contact invariant, contact homology, whose chain complex is generated by closed Reeb orbits. In particular, I will explain the pitfalls in defining contact homology and discuss my work, in part joint with Hutchings, which provides rigorous constructions and applications to dynamics via geometric methods. This talk will feature numerous graphics to acclimate people to the realm of contact geometry.
 
−   
−  ===Justin Hsu (Madison)===
 
−   
−  Title: From Couplings to Probabilistic Relational Program Logics
 
−   
−  Abstract: Many program properties are relational, comparing the behavior of a program (or even two different programs) on two different inputs. While researchers have developed various techniques for verifying such properties for standard, deterministic programs, relational properties for probabilistic programs have been more challenging. In this talk, I will survey recent developments targeting a range of probabilistic relational properties, with motivations from privacy, cryptography, and machine learning. The key idea is to meld relational program logics with an idea from probability theory, called probabilistic couplings. The logics allow a highly compositional and surprisingly general style of program analysis, supporting clean proofs for a broad array of probabilistic relational properties.
 
−   
−  === Kavita Ramanan (Brown) ===
 
−  Title: Tales of Random Projections
 
−   
−  Abstract: The interplay between geometry and probability in highdimensional spaces is a subject of active research. Classical theorems in probability theory such as the central limit theorem and Cramer’s theorem can be viewed as providing information about certain scalar projections of highdimensional product measures. In this talk we will describe the behavior of random projections of more general (possibly nonproduct) highdimensional measures, which are of interest in diverse fields, ranging from asymptotic convex geometry to highdimensional statistics. Although the study of (typical) projections of highdimensional measures dates back to Borel, only recently has a theory begun to emerge, which in particular identifies the role of certain geometric assumptions that lead to better behaved projections. A particular question of interest is to identify what properties of the highdimensional measure are captured by its lowerdimensional projections. While fluctuations of these projections have been studied over the past decade, we describe more recent work on the tail behavior of multidimensional projections, and associated conditional limit theorems.
 
   
 == Past Colloquia ==   == Past Colloquia == 
   
 [[Colloquia/BlankBlank]]   [[Colloquia/BlankBlank]] 
 +  
 +  [[Colloquia/Spring2019Spring 2019]] 
   
 [[Colloquia/Fall2018Fall 2018]]   [[Colloquia/Fall2018Fall 2018]] 