• Speaker: Soumyashant Nayak, University of Pennsylvania
• Title: Analyticity in Operator Algebras
• Date: 08/20/2018
• Time: 11:00 AM - 12:00 PM
• Place: C517 Wells Hall

The title of this talk is borrowed from a seminal paper by Arveson discussing non-commutative analogues of the Hardy space H^∞(T) via the so-called subdiagonal algebras. Subdiagonal algebras are a family of non-self-adjoint operator algebras which give a common perspective to the study of some triangular operator algebras (for example, the algebra of block upper triangular matrices in M_n(C)), Dirichlet function algebras, etc. The first part of the talk will be about a non-commutative version of inner-outer factorization in finite maximal subdiagonal algebras. We will then discuss a proof of a version of Jensen's inequality in this setting which relates to some classical results by Szegö.

• Speaker: Gerard Awanou, University of Illinois, Chicago
• Title: Discrete Aleksandrov solutions of the Monge-Ampere equation
• Date: 08/31/2018
• Time: 4:10 PM - 5:00 PM
• Place: 1502 Engineering Building

A discrete analogue of the Dirichlet problem of the Aleksandrov theory of the Monge-Amere equation is derived in this paper. The discrete solution is not required to be convex, but only discrete convex in the sense of Oberman. We prove that the uniform limit on compact subsets of discrete convex functions which are uniformly bounded and which interpolate the Dirichlet boundary data is a continuous convex function which satisfies the boundary condition strongly. The domain of the solution needs not be uniformly convex. We obtain the first proof of convergence of a wide stencil finite difference scheme to the Aleksandrov solution of the elliptic Monge-Ampere equation when the right hand side is a sum of Dirac masses. The discrete scheme we analyze for the Dirichlet problem, when coupled with a discretization of the second boundary condition,  as proposed by Benamou and Froese, can be used to get a good initial guess for geometric methods solving optimal transport between two measures. 

• Speaker: Daping Weng, MSU
• Title: Cluster Donaldson-Thomas Transformation of Grassmannian
• Date: 09/06/2018
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall

Abstract: On the one hand, there is a 3d Calabi Yau category with stability conditions associated to a quiver without loops or 2-cycles with generic potential, and one can study its Donaldson-Thomas invariants. On the other hand, such a quiver also defines a cluster Poisson variety, which is constructed by gluing a collection of algebraic tori in a certain way governed by combinatorics. In certain cases, the Donaldson-Thomas invariants of the former category can be captured by an automorphism on the latter space. In this talk, I will recall the cluster Poisson structure on the moduli space of configurations of points in a projective space, and state my result on constructing the corresponding cluster Donaldson-Thomas transformation, and give a new proof of Zamolodchikov’s periodicity conjecture in the $A_m\boxtimes A_n$ cases as an application. If time permits, I will also talk about the generalization of this result to double Bruhat cells.

• Speaker: Nick Ovenhouse, MSU
• Title: Hochschild Cohomology
• Date: 09/10/2018
• Time: 1:00 PM - 1:50 PM
• Place: C517 Wells Hall

I will give the basic definitions of Hochschild cohomology, and discuss interpretations of the first few cohomology groups H^0, H^1, and H^2. Time permitting, I will discuss how the groups H^2 and H^3 are related to formal deformations of algebras and quantization of Poisson brackets.

• Speaker: Leonardo Abbrescia, MSU
• Title: Newton's method and periodic solutions of nonlinear wave equations
• Date: 09/13/2018
• Time: 1:00 PM - 2:00 PM
• Place: C304 Wells Hall

We will introduce the paper of Walter Craig and C. E. Wayne of the same name as the title of the talk. We will hopefully cover the first eleven pages.

• Speaker: Dylan Rupel, MSU
• Title: The Combinatorics of Compatible Pairs
• Date: 09/13/2018
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall

Abstract: Compatible subsets of edges in a maximal Dyck path were introduced by Lee, Li, and Zelevinsky as a tool for constructing nice bases for rank two cluster algebras. In this talk, I will present a generalization of this combinatorics and give two applications. The first application is a combinatorial construction of non-commutative rank two generalized cluster variables which proves a conjecture of Kontsevich. The second application gives a combinatorial description of the cells in an affine paving of rank two quiver Grassmannians, this part is joint work with Thorsten Weist.

• Speaker: Dongwook Lee, University of California, Santa Cruz
• Title: New Polynomial-free, Variable High-order Methods using Gaussian Process Modeling for CFD
• Date: 09/14/2018
• Time: 4:10 PM - 5:00 PM
• Place: 1502 Engineering Building

In this talk, an entirely new class of high-order numerical algorithms for computational fluid dynamics is introduced. The new method is based on the Gaussian Processes (GP) modeling that generalizes the Gaussian probability distribution. The new approach is to adopt the idea of the GP prediction technique which utilizes the covariance kernel functions and use it to interpolate and/or reconstruct high-order approximations for computational fluid dynamics simulations. The new GP high-order method is proposed as a new numerical high-order formulation in finite difference and finite volume frameworks, alternative to the conventional polynomial-based approaches.

• Speaker: Selman Akbulut, MSU
• Title: Where do Seiberg-Witten equations come from?
• Date: 09/17/2018
• Time: 4:10 PM - 5:30 PM
• Place: C304 Wells Hall

The question in title is akin to asking where the equation of motion of a free falling object a + bt + 1/2 gt^2 in 3-space come from? then discovering that the "objects fall with constant acceleration" rule. Similarly, we derive Seiberg-Witten equations (which also have a linear part and a quadratic part) from the deformation equations of an "isotropic associative submanifold" of a complex G_2 Manifold. For this, we will define the notion of complex G_2 manifold and notion of complexification of a G_2 manifold (this is a joint work with Ustun Yildirim).

• Speaker: Zhe Zhang (Alan)
• Title: Elliptic Regularity of J-Holomorphic Curves
• Date: 09/19/2018
• Time: 4:00 PM - 4:50 PM
• Place: A202 Wells Hall

One of the fundamental estimates for the L^p theory of elliptic operators is Calderon-Zygmund inequality. I’ll follow Mcduff & Salamon’s book for the proof of regularity theorem, raising the order of nonlinear Cauchy Riemann equation and making use of mean value property.

• Speaker: Matthew Mills, MSU
• Title: Green sequences and local-acyclicity.
• Date: 09/20/2018
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall

In 2014 it was conjectured that the equality of the cluster algebra and upper cluster algebra is equivalent to the existence of a maximal green sequence. In this talk we will discuss a stronger result for cluster algebras from mutation-finite quivers with an emphasis on surface cluster algebras. Specifically we show that for all quivers from surface cluster algebras there exists a maximal green sequence if and only if the cluster algebra is equal to the cluster algebra if and only if the cluster algebra is locally-acyclic. We will also provide a counterexample to show that the result does not hold in general.

• Speaker: Jeff Schenker
• Title: NSF Fellowship Info Session
• Date: 09/21/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Chuangtian Guan, MSU
• Title: Witt Schemes and Witt Vectors
• Date: 09/24/2018
• Time: 1:00 PM - 1:50 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Wenchuan Tian, MSU
• Title: Newton's method and periodic solutions of nonlinear wave equations
• Date: 09/27/2018
• Time: 1:00 PM - 2:00 PM
• Place: C304 Wells Hall

We will cover pages 12 - 23 of the paper by Walter Craig and C.E. Wayne of the same title. These pages cover section 2.4 until the end of the proof of Lemma 3.3.

• Speaker: 
• Title: Joint meeting with Notre Dame: open problem session
• Date: 09/27/2018
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

Abstract: we will discuss open problems in Cluster Algebras theory

• Speaker: Kursat Sozer, IU
• Title: Extended HQFTs in dimension 2
• Date: 10/01/2018
• Time: 4:10 PM - 5:30 PM
• Place: C304 Wells Hall

Topological quantum field theories (TQFTs), inspired by theoretical physics, produce manifold invariants behaving well under gluing. For every discrete group G, homotopy quantum field theories (HQFTs) are G-equivariant versions of TQFTs. In this talk we define and classify 2-dimensional extended HQFTs by generalizing methods introduced for TQFTs by Chris Schommer-Pries in 2009. We list generators and relations for the extended G-equivariant bordism bicategory and use them to classify 2-dimensional extended HQFTs.

• Speaker: Alex Waldron, MSU
• Title: Introduction to the harmonic map problem
• Date: 10/03/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

First in a series of talks covering existence and regularity results for harmonic maps between manifolds. (Reference: Lin and Wang's book.)

• Speaker: N. K. Nikolski, University of Bordeaux
• Title: V.Ya.Kozlov's completeness problem
• Date: 10/03/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

In 1948-1950, V.Ya.Kozlov (1914-2007) stated a series of interesting geometric properties of dilated systems D(f)= {f(kx): k= 1,2,...} in the spaces L^p(0,1). Since that, no proofs were published. In particular, for a Rademacher-Haar-Walsh type generator f= 2-periodic odd extension of the indicator function of (0,a), 0<a<1, the system D(f) was claimed to be complete/incomplete for many particular values of a. We prove all Kozlov's statements and several new, as well as discuss other geometric properties of D(f).

• Speaker: Artem Kotelskiy, Indiana University
• Title: Khovanov homology and Bar-Natan's deformation via immersed curves in the 4-punctured sphere.
• Date: 10/04/2018
• Time: 2:00 PM - 2:50 PM
• Place: C304 Wells Hall

We will describe a geometric interpretation of Khovanov homology and its deformation due to Bar-Natan as Lagrangian Floer homology of two immersed curves in the 4-punctured 2-sphere S^2 \ 4pt. We will first start with a certain cobordism theoretic algebra H, where elements are all cobordisms between two trivial tangles )( and = up to certain relations. The central point then will be the observation that this algebra is isomorphic to an algebra B = Fuk(a0, a1), whose elements are generators of wrapped Lagrangian Floer complexes between two arcs a0 and a1 inside S^2 \ 4pt. The results will follow because D structures over H give Khovanov/Bar-Natan invariants for 4-ended tangles, and D structures over B give curves in S^2 \ 4pt (due to [Haiden, Katzarkov, Kontsevich]). The construction is originally inspired by a result of [Hedden, Herald, Hogancamp, Kirk], which embeds 4-ended reduced Khovanov arc algebra (or, equivalently, Bar-Natan dotted cobordism algebra) into the Fukaya category of the 4-punctured sphere. This is joint work with Liam Watson and Claudius Zibrowius.

• Speaker: Yang Yang, Michigan State University
• Title: Some inverse source and coefficient problems for the wave operators (special colloquium)
• Date: 10/04/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Inverse problems seek to infer causal factor from the resulting observation, and waves are among the most prevalent and significant observations in nature. In this talk, we will discuss two inverse problems for the acoustic wave equation and its generalizations. The first is an inverse source problem where one attempts to determine an instantaneous source from the boundary Dirichlet data. We give sharp conditions on unique and stable determination, and derive an explicit reconstruction formula for the source. The second is an inverse coefficient problem on a cylinder-like Lorentzian manifold (M,g) for the Lorentzian wave operator perturbed by a vector field A and a function q. We show that local knowledge of the Dirichlet-to-Neumann map (DN-map) stably determines the jets of (g,A,q) up to gauge transformations, and global knowledge of the DN-map stably determines the lens relation of g as well as the light ray transforms of A and q. This is based on joint work with P. Stefanov.

• Speaker: Charlotte Ure, MSU
• Title: Étale Cohomology and its Applications to Curves
• Date: 10/08/2018
• Time: 1:00 PM - 1:50 PM
• Place: C517 Wells Hall

Étale cohomology was originally introduced by Grothendieck in the 1960s as a tool for solving the Weil conjectures. Since then it has proven very useful in algebraic and arithmetic geometry. In my talk, I will introduce the notion of Grothendieck topology, étale site, and étale cohomology. I will then explore the cohomology of curves and briefly describe some applications. This talk will be accessible to all levels.

• Speaker: Selman Akbulut, MSU
• Title: A simple family of infinitely many absolutely exotic manifolds
• Date: 10/08/2018
• Time: 4:10 PM - 5:30 PM
• Place: C304 Wells Hall

I wıll demonstrate a smooth 4-manifold M, obtained by attaching a 2-handle to B^4 along a certain knot K in S^3, which admits infinitely many absolutely exotic copies M_n, n=0,1,2.., such that each copy M_n is obtained by attaching 2-handle to a fixed compact smooth contractible manifold W along its boundary Y, along the iterates f^{n}(c) of a knot c in Y by a diffeomorphism f: Y---> Y. This generalizes the example I gave in “An exotic 4-manifold, Jour. of Diff. Geom. 33, (1991)” which corresponds to the n=1 case.

• Speaker: Sanjay Kumar
• Title: Turaev-Viro invariants via quantum representations of the mapping class group
• Date: 10/10/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

The Turaev-Viro invariants are an infinite family of real valued 3-manifold invariants originally defined by state sums of a triangulation. Using SO(3)-TQFT, I will demonstrate an equivalent formulation in terms of traces of quantum representations and discuss its possible advantages in studying mapping tori of surfaces.

• Speaker: Vitali Vougalter, U Toronto
• Title: Existence in the sense of sequences of stationary solutions for some non-Fredholm integro-differential equations
• Date: 10/11/2018
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall

We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in appropriate H^2 spaces. It is shown that, under reasonable technical conditions, the convergence in L^1 of the integral kernels implies the existence and convergence in H^2 of solutions. The nonlocal elliptic equations involve second order differential operators with and without the Fredholm property.

• Speaker: Sung-Soo Byun, Seoul National University
• Title: Annulus SLE partition functions and martingale-observables
• Date: 10/11/2018
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall

In this talk, I will introduce a version of conformal field theory (CFT) and explain its implementations to SLE theory in a doubly connected domain. The basic fields in these implementations are one-parameter family of Gaussian free fields whose boundary conditions are given by a weighted combination of Dirichlet boundary condition and excursion-reflected one. After explaining basic notions in CFT such as OPE families of central charge modifications of the Gaussian free field and presenting certain equations including a version of Eguchi-Ooguri and Ward’s equations, I will outline the relation between CFT and SLE theory. As an application, I will explain how to apply the method of screening to find Euler integral type solutions to the parabolic partial differential equations for the annulus SLE partition functions introduced by Zhan and present a class of SLE martingale-observables associated with these solutions. This is based on joint work with Nam-Gyu Kang and Hee-Joon Tak.

• Speaker: Deanna Needell, University of California, Los Angeles
• Title: Simple Classification from Binary Data
• Date: 10/11/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Binary, or one-bit, representations of data arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this talk, we provide a brief background to sparsity and 1-bit measurements, and then present new results on the problem of data classification from binary data that proposes a framework with low computation and resource costs. We illustrate the utility of the proposed approach through stylized and realistic numerical experiments, provide a theoretical analysis for a simple case, and discuss future directions.

• Speaker: Woong Bae Park, MSU
• Title: Regularity of minimizing harmonic maps in general dimensions
• Date: 10/17/2018
• Time: 2:00 PM - 3:30 PM
• Place: C304 Wells Hall

First talk on Schoen-Uhlenbeck partial regularity theorem for minimizing harmonic maps.

• Speaker: Siddhi Krishna, Boston College
• Title: Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
• Date: 10/18/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

The L-Space Conjecture is taking the low-dimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3-manifold Y. In particular, it predicts a 3-manifold Y isn't "simple" from the perspective of Heegaard-Floer homology if and only if Y admits a taut foliation. The reverse implication was proved by Ozsvath and Szabo. In this talk, we'll present a new theorem supporting the forward implication. Namely, we'll use branched surfaces to build taut foliations for manifolds obtained by surgery on positive 3-braid closures. As an example, we'll construct taut foliations in every non-L-space obtained by surgery along the P(-2,3,7) pretzel knot. No background in Heegaard-Floer or foliation theories will be assumed.

• Speaker: Erkan Nane, Auburn University
• Title: Blow-up Results for Space--time Fractional Dynamics
• Date: 10/18/2018
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall

Linked Abstract

ABSTRACT. Consider non-linear time-fractional stochastic reaction-diffusion equations of the following type, $$ \partial^\beta_tu_t(x)=-\nu(-\Delta)^{\alpha/2} u_t(x)+I^{1-\beta}_t[b(u)+ \sigma(u)\stackrel{\cdot}{F}(t,x)] $$ in $(d+1)$ dimensions, where $\nu>0, \beta\in (0,1)$, $\alpha\in (0,2]$. The operator $\partial^\beta_t$ is the Caputo fractional derivative while $-(-\Delta)^{\alpha/2} $ is the generator of an isotropic $\alpha$-stable L\'evy process and $I^{1-\beta}_t$ is the Riesz fractional integral operator. The forcing noise denoted by $\stackrel{\cdot}{F}(t,x)$ is a Gaussian noise. These equations might be used as a model for materials with random thermal memory. We derive non-existence (blow-up) of global random field solutions under some additional conditions, most notably on $b$, $\sigma$ and the initial condition. Our results complement those of P. Chow in ``P.-L. Chow. Unbounded positive solutions of nonlinear parabolic It$\hat{o}$ equations. Commun. Stoch. Anal., 3(2)(2009), 211--222.'' and ``P.-L. Chow. Explosive solutions of stochastic reaction-diffusion equations in mean $l_{p}$-norm. J. Differential Equations, 250(5) (2011), 2567--2580.'' and Foondun and Parshad ``M. Foondun and R. Parshad, On non-existence of global solutions to a class of stochastic heat equations. Proc. Amer. Math. Soc. 143 (2015), no. 9, 4085--4094'', among others. The results presented are our recent joint work with Sunday Asogwa, Mohammud Foondun, Wei Liu, and Jebessa Mijena.

• Speaker: Min Hoon Kim, KIAS
• Title: A family of freely slice good boundary links
• Date: 10/18/2018
• Time: 3:10 PM - 4:00 PM
• Place: C304 Wells Hall

The still open topological surgery conjecture for 4-manifolds is equivalent to the statement that all good boundary links are freely slice. In this talk, I will show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all previously known methods for freely slicing good boundary links with two or more components, and provides new freely slice links. This is joint work with Jae Choon Cha and Mark Powell.

• Speaker: Paul Bendich, Duke University and Geometric Data Analytics
• Title: Topology and Geometry for Tracking and Sensor Fusion
• Date: 10/19/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Many systems employ sensors to interpret the environment. The target-tracking task is to gather sensor data from the environment and then to partition these data into tracks that are produced by the same target. The goal of sensor fusion is to gather data from a heterogeneous collection of sensors (e.g, audio and video) and fuse them together in a way that enriches the performance of the sensor network at some task of interest. This talk summarizes two recent efforts that incorporate mildly sophisticated mathematics into the general sensor arena. First, a key problem in tracking is to 'connect the dots:' more precisely, to take a piece of sensor data at a given time and associate it with a previously-existing track (or to declare that this is a new object). We use topological data analysis (TDA) to form data-association likelihood scores, and integrate these scores into a well-respected algorithm called Multiple Hypothesis Tracking. Tests on simulated data show that the TDA adds significant value over baseline, especially in the context of noisy sensor data. Second, we propose a very general and entirely unsupervised sensor fusion pipeline that uses recent techniques from diffusion geometry and wavelet theory to fuse time series of arbitrary dimension arising from disparate sensor modalities. The goal of the pipeline is to differentiate classes of time-ordered behavior sequences, and we demonstrate its performance on a well-studied digit sequence database. This talk represents joint work with many people. including Chris Tralie, Nathan Borggren, Sang Chin, Jesse Clarke, Jonathan deSena, John Harer, Jay Hineman, Elizabeth Munch, Andrew Newman, Alex Pieloch, David Porter, David Rouse, Nate Strawn, Adam Watkins, Michael Williams, and Peter Zulch.

• Speaker: Ekaterina Rapinchuk
• Title: Auction Dynamics for Semi-Supervised Data Classification
• Date: 10/23/2018
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall

We reinterpret the semi-supervised data classification problem using an auction dynamics framework (inspired by real life auctions) in which elements of the data set make bids to the class of their choice. This leads to a novel forward and reverse auction method for data classification that readily incorporates class-size constraints into an accurate and efficient algorithm requiring remarkably little training/labeled data. We prove that the algorithm is unconditionally stable.

• Speaker: Alex Waldron
• Title: Epsilon-regularity of harmonic maps
• Date: 10/24/2018
• Time: 2:00 PM - 3:30 PM
• Place: C304 Wells Hall

Proof of the key partial regularity theorem for minimizing (and stationary) harmonic maps, and bound on Hausdorff measure of the singular set.

• Speaker: Maxim Gilula, MSU
• Title: l^2 decoupling with vanishing curvature
• Date: 10/24/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

I will discuss recent progress on decoupling for curves with vanishing curvature.

• Speaker: 
• Title: MSU-ND Summit @ ND
• Date: 10/25/2018
• Time: 3:00 PM - 5:00 PM
• Place: 

We will be heading to Notre Dame to discuss open problems in the field. We will meet in room Hurley 258.

• Speaker: Shahriar Mirzadeh, MSU
• Title: Homogeneous dynamics and applications to number theory
• Date: 10/30/2018
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

Abstract: Homogeneous dynamics is another name for the theory of flows on homogeneous spaces, or homogeneous flows. It has been realized that some problems in number theory can be solved using Homogeneous dynamics. In this talk, we are going to see some of the basics of this theory. We will talk about Ratner’s theorem that is one of the most important results in Homogeneous Dynamics and will use it to provide the sketch of Margulis proof of “Oppeinheim Conjecture” in number theory. This is an introductory talk accessible to general audiences.

• Speaker: Kristina Skreb
• Title: TBA
• Date: 10/31/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Andrew Krause, MSU
• Title: TBA (special colloquium)
• Date: 11/01/2018
• Time: 10:00 AM - 11:00 AM
• Place: C304 Wells Hall

TBA

• Speaker: Keith Promislow, Chair, MSU
• Title: Special Presentation By Chair
• Date: 11/01/2018
• Time: 2:30 PM - 3:30 PM
• Place: B122 Wells Hall

Five years as Chair

• Speaker: Rustum Choksi, McGill University
• Title: Nonlocal Geometric Variational Problems: Isotropic and Anisotropic Extensions of Gamow's Liquid Drop Problem and Beyond
• Date: 11/01/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

The liquid drop (LD) model, an old problem of Gamow for the shape of atomic nuclei, has recently resurfaced within the framework of the modern calculus of variations. The problem takes the form of a nonlocal isoperimetric problem on all 3-space with nonlocal interactions of Coulombic type. In this talk, we first state and motivate the LD problem, and then summarize the state of the art for global minimizers. We then address certain recent anisotropic variants of the LD problem in the small mass regime, with a particular focus on the minimality of the Wulff shape. In the second half of the talk, we address a related nonlocal geometric problem based solely on competing interaction potentials of algebraic type. This problem is directly related to a wide class of self-assembly/aggregation models for interacting particle systems (eg. swarming). This talk includes joint work with Almut Burchard (Toronto), Robin Neumayer (IAS and Northwestern), and Ihsan Topaloglu (Virginia Commonwealth).

• Speaker: Telma Gracias
• Title: TBA (special colloquium)
• Date: 11/05/2018
• Time: 10:00 AM - 11:00 AM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Boris Shapiro, Stockholm University
• Title: Around Waring problem for homogeneous polynomials
• Date: 11/07/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

Waring problem for homogeneous polynomials (forms) asks to represent a given form of degree k*d as a sum of d-th powers of forms of degree k. The main objective is to find a presentation with a small number of summands. The classical case going back to J.J. Sylvester deals with k=1 and binary forms. We will survey some of the results in this area and pose some elementary looking open problems. No preliminary knowledge of the topic is required

• Speaker: Abhishek Mallick
• Title: Equivariant Floer Homology
• Date: 11/07/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

We will discuss constructions given by Seidel-Smith and Hendricks-Lipshitz-Sarkar.

• Speaker: Irina Holmes, MSU and Texas A&M
• Title: Bellman and Bollobas Functions
• Date: 11/07/2018
• Time: 5:10 PM - 6:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Jared Speck
• Title: Singularity Formation in General Relativity
• Date: 11/08/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

The celebrated Hawking–Penrose theorems are breakdown results for solutions to the Einstein equations of general relativity, which are a system of highly nonlinear wave-like PDEs. These theorems show that, under appropriate assumptions on the matter model, a large, open set of initial data lead to geodesically incomplete solutions. However, these theorems are “soft” in that they do not yield any information about the nature of the incompleteness, leaving open the possibilities that i) it is tied to the blowup of some invariant quantity (such as curvature) or ii) it is due to a more sinister phenomenon, such as incompleteness stemming from lack of information for how to uniquely continue the solution (this is roughly known as the formation of a Cauchy horizon). In various works, some joint with I. Rodnianski, we have obtained the first results in more than one spatial dimension that eliminate the ambiguity for an open set of initial data: for the solutions that we studied, the incompleteness is tied to the blowup of various spacetime curvature scalars along a spacelike hypersurface. Physically, this phenomenon corresponds to the stability of the Big Bang and/or Big Crunch singularities. From an analytic perspective, the main theorems are stable blowup results for quasilinear systems of elliptic-hyperbolic PDEs. In this talk, I will provide an overview of these results and explain how they are tied to some of the main themes of investigation by the mathematical general relativity community. I will also discuss the role of geometric and gauge considerations in the proofs, as well as intriguing connections to other problems concerning stable singularity formation.

• Speaker: Wenrui Hao, Pennsylvania State University
• Title: Computational modeling for cardiovascular risk evaluation
• Date: 11/09/2018
• Time: 4:10 PM - 5:00 PM
• Place: 1502 Engineering Building

Atherosclerosis, the leading cause of death in the United State, is a disease in which a plaque builds up inside the arteries. The LDL and HDL concentrations in the blood are commonly used to predict the risk factor for plaque growth. In this talk, I will describe a recent mathematical model that predicts the plaque formation by using the combined levels of (LDL, HDL) in the blood. The model is given by a system of partial differential equations within the plaque with a free boundary. This model is used to explore some drugs of regression of a plaque in mice, and suggest that such drugs as used for mice may also slow plaque growth in humans. Some mathematical questions, inspired by this model, will also be discussed. I will also mention briefly some related projects about abdominal aortic aneurysm (AAA) and red blood cell aggregation, which would have some potential blood biomarkers for diagnosis of AAA.

• Speaker: Joshua Ruiter, MSU
• Title: Universal Central Extensions
• Date: 11/12/2018
• Time: 1:00 PM - 2:00 PM
• Place: C517 Wells Hall

I'll define universal central extensions of groups, and prove a criterion for a central extension to be universal. Time permitting, I'll connect this to the 2nd algebraic K-group of a ring, and a certain group cohomology.

• Speaker: Vincent Bouchard , University of Alberta
• Title: W-algebra constraints and higher Airy structures
• Date: 11/13/2018
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

Virasoro constraints are omnipresent in enumerative geometry. Recently, Kontsevich and Soibelman introduced a generalization of Virasoro constraints in the form of Airy structures. It can also be understood as an abstract framework underlying the topological recursion of Chekhov, Eynard and Orantin. In this talk I will explain how the triumvirate of Virasoro constraints, Airy structures and topological recursion can be generalized to W-algebra constraints, higher Airy structures and higher topological recursion. The resulting formalism includes as a special case the W-algebra constraints satisfied by generating functions for intersection numbers on the moduli space of r-spin curves, but is much more general. This is joint work with Gaetan Borot, Nitin Chidambaram and Dmitry Noschenko.

• Speaker: Dapeng Zhan, MSU
• Title: Two-curve Green’s function for 2-SLE
• Date: 11/15/2018
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall

A 2-SLE$_\kappa$, $\kappa\in(0,8)$, is a pair of random curves $(\eta_1,\eta_2)$ in a simply connected domain $D$ connecting two pairs of boundary points such that conditioning on any curve, the other is a chordal SLE$_\kappa$ curve in a complement domain. We prove that, for the exponent $\alpha=\frac{(12-\kappa)(\kappa+4)}{8\kappa}$, for any $z_0\in D$, the limit $\lim_{r\to 0^+}r^{-\alpha}\mathbb{P}[\mbox{dist}(\eta_j,z_0)<r,j=1,2]$ converges to a positive number, called the two-curve Green’s function. To prove the convergence, we transform the original problem into the study of a two-dimensional diffusion process, and use orthogonal polynomials to derive its transition density and invariant density.

• Speaker: Dominique Maldague, UC Berkeley
• Title: TBA
• Date: 11/16/2018
• Time: 2:10 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Keshav Sutrave
• Title: Eells-Sampson's Theorem
• Date: 11/21/2018
• Time: 12:30 PM - 2:00 PM
• Place: C304 Wells Hall

1964 classic existence result for harmonic maps with non-positively curved target manifold, using heat flow method.

• Speaker: Darryl Yong, Harvey Mudd College
• Title: Active Learning 2.0: Being Intentionally Inclusive
• Date: 11/27/2018
• Time: 1:30 PM - 3:00 PM
• Place: 252 EH

Active learning has many documented benefits both for students and instructors. Moreover, there is increasing evidence that it disproportionately benefits women, students of color, and students who were previously denied the same learning opportunities as others. However, the empirical evidence for this disproportionate benefit doesn't explain why it happens, nor does it guarantee that all students will benefit from active learning. In fact, my own experience with active learning is that it is difficult to do well and sometimes it can have detrimental effects on students if we're not careful. So, we should aim not just for active learning, but learning that is both active and inclusive. We'll discuss some principles and practical strategies for making active learning more inclusive.

• Speaker: Alexander Volberg, MSU
• Title: Improving L^1 Poincar\'e inequality on Hamming cube
• Date: 11/28/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

L^1 Poincar\'e inequality on hypercube is related to many interesting questions in random graph theory (like Margoulis graph connectivity theorem, e.g.). The sharp constant is unknown, but I will show how to improve the previously known constant \pi/2 obtained by Ben Efraim and Lust--Piquard by using non-commutative harmonic analysis. The approach will be probabilistic and luckily commutative. For Gaussian space the constant is known, it is \sqrt{\pi/2}, and the short proof belong to Maurey--Pisier.

• Speaker: Dominic Culver, University of Illinois Urbana-Champaign
• Title: TBA
• Date: 11/29/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Rongrong Lin , Sun Yat-sen University
• Title: Machine Learning with Reproducing Kernels
• Date: 11/30/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

Reproducing kernel Hilbert spaces (RKHSs) are Hilbert spaces of functions on which point evaluation functionals are continuous. Thanks to the existence of an inner product, RKHSs are well-understood in functional analysis. Successful and important machine learning methods based on RKHSs include support vector machines, regularization networks and kernel-based approximation. In the past decade, there has been emerging interest in constructing reproducing kernel Banach spaces (RKBSs) for applied and theoretical purposes for instance sparse approximation. Recently, we propose a generic definition of RKBS and a framework of constructing RKBSs that unifies existing constructions in the literature, and leads further to new RKBSs. As a by-product, the space C([0,1]) of all continuous functions on the interval [0,1] is an RKBS. Motivated by sparse multi-task learning, we constructed a class of vector-valued RKBSs with the l1 norm based on multi-task admissible kernels. The relaxed linear representer theorem holds for regularization networks in the obtained spaces if and only if the Lebesgue constant of kernels is uniformly bounded. A class of translation-invariant kernels of limited smoothness admissible for construction are given. Numerical experiments demonstrate the advantages of the proposed construction and regularization models. This talk is based on two joint papers with Prof. Guohui Song (Clarkson University), Haizhang Zhang (Sun Yat-sen University), and Jun Zhang (University of Michigan).

• Speaker: Zhe Zhang
• Title: TBD
• Date: 12/05/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

No abstract available.

• Speaker: Noam Elkies, Harvard University
• Title: TBA
• Date: 12/13/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.