• 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: Woong Bae Park
• Title: Compactness properties of harmonic maps
• Date: 10/31/2018
• Time: 2:00 PM - 4:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Wenchuan Tian
• Title: A Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature
• Date: 10/31/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

Gromov conjectured that sequences of compact Riemannian manifolds with positive scalar curvature should have subsequences which converge in the intrinsic flat sense to limit spaces with some generalized notion of scalar curvature. In light of three dimensional examples discovered jointly with Basilio and Dodziuk, Sormani suggested that one add an hypothesis assuming a uniform lower bound on the area of a closed minimal surface. We have proven this revised conjecture in the setting where the sequence of manifolds are 3 dimensional rotationally symmetric warped product manifolds. This is a project given by professor Christina Sormani, and is joint work with Jiewon Park and Changliang Wang.

• Speaker: Yuanqi Wang
• Title: Moduli space of G2-instantons on 7-dimensional product manifolds
• Date: 11/01/2018
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall

$G_2$-instantons are 7-dimensional analogues of flat connections in dimension 3. It is part of Donaldson-Thomas’ program to generalize the fruitful gauge theory in dimensions 2,3,4 to dimensions 6,7,8. The moduli space of $G_2$-instantons, with virtual dimension 0, is expected to have interesting geometric structure and yield enumerative invariant for the underlying 7-dimensional manifold. In this talk, in some reasonable special cases and a fairly complete manner, we will describe the relation between the moduli space of $G_2$-instantons and an algebraic geometry moduli on a Calabi-Yau 3-fold.

• Speaker: Dylan Rupel, MSU
• Title: Cluster Monomials and Theta Bases via Scattering Diagrams
• Date: 11/01/2018
• 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: Jianlin Cheng, University of Missouri
• Title: Data-driven computational modeling of 3D structures of genomes
• Date: 11/02/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

The three-dimensional (3D) structure of a genome is important for genome folding, genome function, genome methylation, spatial gene regulation, and cell development, but has not been well studied due to lack of experimental techniques for genome structure determination. In this talk, I will present our large-scale computational optimization methods for effectively reconstructing the 3D structure (shape) of the human genome from chromosomal conformation capturing data. The highly scalable algorithms were able to build the highest-resolution structures of human chromosomes to date and one of the first structures of the entire human genome. The computational modeling enables the visualization of the previously unknown 3D shape of the genome consisting of millions of units and opens a new avenue to conduct genomics research in the 3D perspective.

• Speaker: Sue Allen
• Title: MTH 103: Large Lecture Updates + ULA Management
• Date: 11/05/2018
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall

No abstract available.

• Speaker: Gorapada Bera
• Title: Federer's dimension reduction argument
• Date: 11/07/2018
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

Ch. 3 of Leon Simon's book

• Speaker: Guozhen Lu, University of Connecticut; Nobody Else
• Title: Fourier analysis on hyperbolic spaces and sharp higher order Hardy-Sobolev-Maz'ya inequalities
• Date: 11/07/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

In this talk, we will describe some recent works on the sharp higher order Hardy-Sobolev-Maz'ya and Hardy-Adams inequalities on hyperbolic balls and half spaces. The relationship between the classical Sobolev inequalities and the Hardy-Sobolev-Maz'ya inequalities for higher order derivatives will be established. Our main approach is to use the Fourier analysis on hyperbolic spaces and Green's function estimates.

• Speaker: Jonathan Campbell, Vanderbilt University
• Title: Topological Hochschild Homology and Higher Characters
• Date: 11/08/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

In this talk I'll explain how Hochschild homology and duality theory in bicategories can be used to obtain interesting Euler characteristic-type invariants in a number of mathematical contexts (all of the terms in the previous sentence will be explained). A topological refinement, using THH, of this reasoning very easily yields interesting fixed point invariants, such as the Lefschetz trace and Reidemeister trace. Using this, one can show that the cyclotomic trace from algebraic K-theory is computing fixed point invariants. Time permitting, I'll explain how zeta functions relate to the above. Prerequisites: an appetite for category theory, and a belief in, but not knowledge of, the stable homotopy category.

• Speaker: Tsz Ho Chan, University of Memphis
• Title: TBA (special colloquium)
• Date: 11/09/2018
• Time: 10:00 AM - 11:00 AM
• Place: C304 Wells Hall

TBA

• Speaker: Jun Kitagawa, MSU
• Title: Optimal transport or: How I learned to stop worrying and grew my own shipping empire
• Date: 11/09/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Optimal transport, a.k.a. the Monge-Kantorovich problem has been an active area of mathematics recently. It is an optimization problem, but has connections to PDEs, geometry, economics, image processing, kinetics, and probability, among other areas. I will start with the discrete optimal transport problem and explain some results about existence, duality, and computation. If time permits, I will discuss the continuous framework and some other variations of the problem.

• Speaker: Leonid Chekhov, MSU
• Title: Introduction to topological recursion
• Date: 11/12/2018
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

I will give a brief description of main ingredients of abstract topological recursion, which is a method for constructing correlation functions in a number of models admitting "genus", or 1/N filtration. I will show how the condition of total symmetricity of the correlation functions naturally leads to algebras of second-order differential operators annihilating the partition function of a model. I will also discuss the transition between global and local models on a spectral curve.

• Speaker: Shahriar Mirzadeh, MSU
• Title: Dimension estimates for the set of points with non-dense orbit in homogeneous spaces
• Date: 11/13/2018
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Abstract: In this talk we study the set of points in a homogeneous space whose orbit escapes the complement of a fixed compact subset. We find an upper bound for the Hausdorff dimension of this set. This extends the work of Kadyrov, where he found an upper bound for the Hausdorff dimension of the set of points whose orbit misses a fixed ball of sufficiently small radius in a compact homogeneous space. We can also use our main result to produce new applications to Diophantine approximation. This is joint work with Dmitry Kleinbock.

• Speaker: Alexey Karapetyants
• Title: On Bergman type spaces of functions of nonstandard growth and some related questions.
• Date: 11/14/2018
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

Abstracts: We study various Banach spaces of holomorphic functions on the unit disc and half plane. As a main question we investigate the boundedness of the corresponding holomorphic projection. We exploit the idea of V.P.Zaharyuta, V.I.Yudovich (1962) where the boundedness of the Bergman projection in Lebesgue spaces was proved using Calderon-Zygmund operators. We treat the cases of variable exponent Lebesgue space, Orlicz space, Grand Lebesgue space and variable exponent generalized Morrey space. The major idea is to show that the approach can be applied to a wide range of function spaces. This opens a door in a sense for introducing and studying new function spaces of Bergman type in complex analysis. We also study the rate of growth of functions near the boundary in spaces under consideration and their approximation by mollifying dilations.

• Speaker: Ian Zemke, Princeton University
• Title: The stabilization distance and knot Floer homology
• Date: 11/15/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

Given a knot K in S^3, we consider the set of oriented surfaces in B^4 which bound K. A natural question is how many stabilizations and destabilizations one must perform to move from one surface to another. Similarly, one may wonder how many double point birth/deaths must occur in a regular homotopy. In this talk, we consider several metrics on the set of surfaces bounding K, based on the number of stabilizations which must occur in a stabilization sequence connecting the two surfaces, or in the minimal number of double points which appear in a generic regular homotopy. We will describe how the link Floer TQFT can be used to construct lower bounds. This is joint work with Andras Juhasz.

• Speaker: Daping Weng, MSU
• Title: More on Scattering Diagram and Theta Functions
• Date: 11/15/2018
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall

Abstract: I will continue the discussion on scattering diagram and theta functions and relate them to the classical cluster theories. I will sketch Gross-Hacking-Keel-Kontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.

• 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: Andrew Krause, MSU
• Title: MTH 133 Labs: Classroom Research and Future Directions
• Date: 11/19/2018
• Time: 5:15 PM - 6:00 PM
• Place: C109 Wells Hall

No abstract available.

• Speaker: Gorapada Bera
• Title: Introduction to Seiberg-Witten Invariants
• Date: 11/21/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

After a brief introduction of Seiberg-Witten equations on closed smooth four manifolds, we will see how moduli space of solutions leads to an oriented compact manifold and a topological invariant (Seiberg-Witten Invariant) for the four manifold. Then for the purpose of computation of this invariant on Kähler manifolds, we will rewrite the equation in terms of complex geometry and see for most of the Kähler Surfaces the answer will be in terms of algebraic geometric criterion of the surface. Most of the technical details will be omitted but some brief sketches will be there. I will follow John Morgan's Book on Seiberg Witten equations.

• 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: Thomas Walpuski
• Title: Quantitative Stratification and the Regularity of Harmonic Maps (part I)
• Date: 11/28/2018
• Time: 2:00 PM - 3:30 PM
• Place: C304 Wells Hall

Cheeger-Naber's 2011 paper (Published in CPAM, 2013).

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

One of the nicer properties a knot can have is to be alternating. These knots tend to be easy to work with, and can give us several nice results about the whole class. Unfortunately, many knots are not alternating, causing general proofs about them to be difficult at best. In this talk, we will take a look at a couple of different ways we can broaden the class of alternating knots, and see what we can get from these different definitions of alternating.

• Speaker: Greg Muller, University of Oklahoma
• Title:  Scattering diagrams of marked surfaces
• Date: 11/29/2018
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall

Every cluster algebra has an associated 'scattering diagram': an affine space endowed with a (possibly very complicated) collection of 'walls'. The structure of this scattering diagram encodes essential information about the cluster algebra's exchange graph, Laurent coefficients, and theta functions. In this talk, I will discuss an ongoing project with Nathan Reading and Shira Viel to construct a scattering diagram associated to a triangulable marked surface. The affine space may be identified with the set of certain `measured laminations' on the surface, and the walls may be identified with certain forbidden subgraphs embedded in the surface, which we call `barricades'.

• Speaker: Estrella Johnson, Virginia Tech
• Title: Taking an Instructional Innovation to Scale: Characterizing, Supporting, and Evaluating Inquiry-Oriented Instruction
• Date: 11/30/2018
• Time: 10:20 AM - 11:10 AM
• Place: C304 Wells Hall

Inquiry-oriented instruction has shown promise in regards to many features of student success, including conceptual understanding, affective gains, and persistence in STEM degrees. However, instructional change is difficult (especially at scale) and the research literature has documented a number of challenges instructors face when shifting their instructional practice. During this talk I will provide a characterization of inquiry-oriented instruction; discuss an instructional support model that was developed to support inquiry-oriented instruction in undergraduate mathematics courses; and present preliminary evaluation findings, drawing on a national sample of content assessment data, collected from 513 students at 46 different institutions. Analysis of this assessment data revealed no difference in the performance of men and women in the comparison sample; however, under the inquiry-oriented treatment, a gender performance difference was present – with men outperforming women. In an effort to understand this finding, I present related research literature on gendered experiences in collaborative settings and our preliminary analysis into the experiences of our students in these inquiry-oriented courses.

• Speaker: Kesong Yan, MSU and Guangxi University of Finance and Economics
• Title: Entropy and Complexity of topological dynamical systems
• Date: 12/04/2018
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

Abstract: In this talk, we will review some results about the topological entropy and complexity for topological dynamical systems. This is a continuation of the talk given in the last week.

• Speaker: Zhe Zhang
• Title: Bott's paper about geometric quantization
• Date: 12/05/2018
• Time: 4:10 PM - 5:00 PM
• Place: A202 Wells Hall

Raoul Bott - "On some recent interactions between mathematics and physics" (1985). It is a mathematical point of view about how quantum phenomena naturally arises when we use Feynman’s idea of path integral and try to give a rigorous definition of the electromagnetic potential. This in turn gives us a new interpretation of a symplectic manifold as space of flat connections over a Riemann surface.

• Speaker: Daping Weng, MSU
• Title: More on Scattering Diagram and Theta Functions
• Date: 12/06/2018
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall

I will continue the discussion on scattering diagram and theta functions and relate them to the classical cluster theories. I will sketch Gross-Hacking-Keel-Kontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.

• Speaker: Ming Tse Paul Laiu, Oak Ridge National Laboratory
• Title: A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations
• Date: 12/07/2018
• Time: 4:10 PM - 5:00 PM
• Place: 1502 Engineering Building

We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization. Under mild assumptions, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering cross-section tends to infinity. The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations. The scheme is tested on well-known benchmark problems and gives promising results.