• 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: Nick Ovenhouse, MSU
• Title: Introduction to Scattering Diagrams
• Date: 10/11/2018
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall

I will give basic definitions of scattering diagrams and wall-crossing automorphims, and finish by showing some examples related to rank-2 cluster algebras.

• 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: 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: Dylan Rupel, MSU
• Title: Cluster Monomials and Theta Bases via Scattering Diagrams
• Date: 10/18/2018
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall

In this talk I will add to Nick’s presentation from last time by describing a portion of the scattering diagram using c-vectors and g-vectors. Then I will present some examples of computing cluster monomials using broken lines. If there is time I will compute an element of the theta basis which is not a cluster monomial.

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

No abstract available.

• 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: AWM Seminar - Applied Mathematics
• Date: 10/23/2018
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall

Dr. Ekaterina Rapinchuk will be giving a talk which will partially be accessible to undergraduates on applied mathematics.

• 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: Irina Holmes, MSU and Texas A&M
• Title: Bellman and Bollobas Functions
• Date: 10/31/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Rustum Choksi, McGill University
• Title: TBA
• Date: 11/01/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Jonathan Campbell, Vanderbilt University
• Title: TBA
• Date: 11/08/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• 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: Dominique Maldague, UC Berkeley
• Title: TBA
• Date: 11/14/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Jun Song, University of Illinois at Urbana-Champaign
• Title: Spectral and Statistical Analyses of Nucleosome Positioning: New Answers to Old Questions
• Date: 11/16/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Nucleosomes form the fundamental building blocks of eukaryotic chromatin, and previous attempts to understand the principles governing their genome-wide distribution have spurred much interest and debate in biology. In particular, the precise role of DNA sequence in shaping local chromatin structure has been controversial. In this talk, I will described categorical spectral analysis methods and statistical physics approaches for rigorously quantifying the contribution of hitherto-debated sequence features to three distinct aspects of genome-wide nucleosome landscape: occupancy, translational positioning, and rotational positioning.

• Speaker: Brandon Bavier
• Title: TBD
• Date: 11/28/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

No abstract available.

• Speaker: Greg Muller, University of Oklahoma
• Title: TBA
• Date: 11/30/2018
• Time: 12:00 AM - 12:00 AM
• Place: C117 Wells Hall

No abstract available.

• Speaker: Lev Tovstopyat-Nelip , Boston College
• Title: TBA
• Date: 12/06/2018
• Time: 2:00 PM - 2:50 PM
• Place: C304 Wells Hall

No abstract available.