• Speaker: Matthew Ballard, University of South Carolina
• Title: Exceptional collections: what they are and where to find them (special colloquium)
• Date: 01/07/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Analogous to orthonormal bases in linear algebra, exceptional collections in triangulated categories are the most atomic means of decomposition. In this talk, we will introduce exceptional collections drawing heavily on examples from noncommutative algebra, algebraic geometry and symplectic geometry. We will then address the question of where (and how) to find them.

• Speaker: Pavlo Pylyavskyy, University of Minnesota
• Title: Zamolodchikov periodicity and integrability (special colloquium)
• Date: 01/11/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

T-systems are certain discrete dynamical systems associated with quivers. They appear in several different contexts: quantum affine algebras and Yangians, commuting transfer matrices of vertex models, character theory of quantum groups, analytic Bethe ansatz, Wronskian-Casoratian duality in ODE, gauge/string theories, etc. Periodicity of certain T-systems was the main conjecture in the area until it was proven by Keller in 2013 using cluster categories. In this work we completely classify periodic T-systems, which turn out to consist of 5 infinite families and 4 exceptional cases, only one of the infinite families being known previously. We then proceed to classify T-systems that exhibit two forms of integrability: linearization and zero algebraic entropy. All three classifications rely on reduction of the problem to study of commuting Cartan matrices, either of finite or affine types. The finite type classification was obtained by Stembridge in his study of Kazhdan-Lusztig theory for dihedral groups, the other two classifications are new. This is joint work with Pavel Galashin.

• Speaker: Goncalo Oliveira, Universidade Federal Fluminense, Rio de Janeiro
• Title: Gauge theory on Aloff-Wallach spaces
• Date: 01/16/2019
• Time: 1:40 PM - 3:00 PM
• Place: C517 Wells Hall

I will describe joint work with Gavin Ball constructing and classifying G2-instantons on Aloff-Wallach spaces, which are the most interesting known examples of compact "nearly-parallel" G2-manifolds.

• Speaker: Daping Weng, MSU
• Title: More on Scattering Diagram and Theta Functions
• Date: 01/17/2019
• 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: Wencai Liu, University of California, Irvine
• Title: Universal arithmetical hierarchy of eigenfunctions for supercritical almost Mathieu operators (special colloquium)
• Date: 01/21/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

The Harper's model is a tight-binding description of Bloch electrons on $\mathbb{Z}^2$ under a constant transverse magnetic field. In 1964, Mark Azbel predicted that both spectra and eigenfunctions of this model have self-similar hierarchical structure driven by the continued fraction expansion of the irrational magnetic flux. In 1976, the hierarchical structure of spectra was discovered numerically by Douglas Hofstadter, and was later observed in various experiments. The mathematical study of Harper's model led to the development of spectral theory of the almost Mathieu operator, with the solution of the Ten Martini Problem partially confirming the fractal structure of the spectrum. In this talk we will present necessary background and discuss the main ideas behind our confirmation (joint with S. Jitomirskaya) of Azbel's second prediction of the structure of the eigenfunctions. More precisely, we show that the eigenfunctions of the almost Mathieu operators in the localization regime, feature self-similarity governed by the continued fraction expansion of the frequency. These results also lead to the proof of sharp arithmetic transitions between pure point and singular continuous spectra, both in the frequency and the phase, as conjectured in 1994.

• Speaker: Rebecca Winarski, University of Michigan
• Title: Solving the Twisted Rabbit Problem using trees
• Date: 01/24/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

The twisted rabbit problem is a celebrated problem in complex dynamics. Work of Thurston proves that up to equivalence, there are exactly three branched coverings of the sphere to itself satisfying certain conditions. When one of these branched coverings is modified by a mapping class, a map equivalent to one of the three coverings results. Which one? After remaining open for 25 years, this problem was solved by Bartholdi-Nekyrashevych using iterated monodromy groups. In joint work with Belk, Lanier, and Margalit, we present an alternate solution using topology and geometric group theory that allows us to solve a more general problem.

• Speaker: Zhe Zhang, MSU
• Title: Harmonic map flow in dimension two, II
• Date: 01/28/2019
• Time: 1:40 PM - 3:00 PM
• Place: C517 Wells Hall

Bubble tree analysis and energy identity.

• Speaker: Tom Parker, MSU
• Title: Convergence modulo diffeomorphisms of maps from Riemann surfaces
• Date: 02/06/2019
• Time: 1:40 PM - 3:00 PM
• Place: C517 Wells Hall

For the theory of both harmonic and holomorphic maps, one needs a notion of convergence maps modulo diffeomorphisms of the domain. I will describe an approach (developed with Woongbae Park) that uses Kuranishi families in place of the standard approach based on bubble tree convergence.

• Speaker: Mihai Tohaneanu, University of Kentucky
• Title: Local energy estimates on black hole backgrounds
• Date: 02/06/2019
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

Local energy estimates are a robust way to measure decay of solutions to linear wave equations. I will discuss several such results on black hole backgrounds, such as Schwarzschild, Kerr, and suitable perturbations converging at various rates, and briefly discuss applications to nonlinear problems. The most challenging geometric feature one needs to deal with is the presence of trapped null geodesics, whose presence yield unavoidable losses in the estimates. This is joint work with Lindblad, Marzuola, Metcalfe, and Tataru.

• Speaker: Elizabeth Munch, MSU
• Title: The Interleaving Distance for a Category with a Flow
• Date: 02/07/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

All data has noise, and rigorously understanding how your analysis fares in the face of that noise requires a notion of a metric. The idea of the interleaving distance arose in the context of generalizing metrics for persistence modules from the field of topological data analysis (TDA). Essentially, the idea is that two objects in a category should be distance 0 if there is an isomorphism between them; the distance between two objects should be "almost" 0 if there is "almost" an isomorphism between them. Placed in the right context, we can measure what we mean by an "almost'' isomorphism and use this to define a distance. Building on the work of Chazal et al.; and Bubenick, Scott, and de Silva, we will discuss the generalization of the notion of the interleaving distance to a so-called "category with a flow". We will show that this generalization provides metrics for many different categories of interest in TDA and beyond, including Reeb graphs, merge trees, phylogenetic trees, and mapper graphs. This work is the result of collaborations with Anastasios Stefanou, Vin de Silva, and Amit Patel.

• Speaker: Xiaodong Wang, MSU
• Title: Harmonic maps and superrigidity (after Mok-Siu-Yeung)
• Date: 02/11/2019
• Time: 1:40 PM - 3:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Albert Ai, UC Berkeley
• Title: Low Regularity Solutions for Gravity Water Waves
• Date: 02/13/2019
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

We consider the local well-posedness of the Cauchy problem for the gravity water waves equations, which model the free interface between a fluid and air in the presence of gravity. It has been known that by using dispersive effects, one can lower the regularity threshold for well-posedness, below that which is attainable by energy estimates alone. This program was initiated for gravity water waves by Alazard-Burq-Zuily, by proving Strichartz estimates with loss. We discuss how these Strichartz estimates, and thus the low regularity threshold, can be sharpened by applying an integration along the Hamilton flow combined with local smoothing estimates.

• Speaker: Melissa Zhang, Boston College
• Title: Localization in Khovanov homology
• Date: 02/14/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

When a topological object admits a group action, we expect that our invariants reflect this symmetry in their structure. This talk will tour the expression of link symmetries in three generations of related invariants: the Jones polynomial; its categorification, Khovanov homology; and the youngest invariant in the family, the Khovanov stable homotopy type, introduced by Lipshitz and Sarkar. I will describe how to use Lawson-Lipshitz-Sarkar's Burnside functor construction of the Lipshitz-Sarkar Khovanov homotopy type to produce localization theorems and Smith-type inequalities for the Khovanov homology of periodic links. This joint work with Matthew Stoffregen.

• Speaker: Nicolas Garcia Trillos, University of Wisconsin-Madison
• Title: Large sample asymptotics of spectra of Laplacians and semilinear elliptic PDEs on random geometric graphs
• Date: 02/15/2019
• Time: 4:10 PM - 5:00 PM
• Place: 1502 Engineering Building

Given a data set $\mathcal{X}=\{x_1, \dots, x_n\}$ and a weighted graph structure $\Gamma= (\mathcal{X},W)$ on $\mathcal{X}$, graph based methods for learning use analytical notions like graph Laplacians, graph cuts, and Sobolev semi-norms to formulate optimization problems whose solutions serve as sensible approaches to machine learning tasks. When the data set consists of samples from a distribution supported on a manifold (or at least approximately so), and the weights depend inversely on the distance between the points, a natural question to study concerns the behavior of those optimization problems as the number of samples goes to infinity. In this talk I will focus on optimization problems closely connected to clustering and supervised regression that involve the graph Laplacian. For clustering, the spectrum of the graph Laplacian is the fundamental object used in the popular spectral clustering algorithm. For regression, the solution to a semilinear elliptic PDE on the graph provides the minimizer of an energy balancing regularization and data fidelity, a sensible object to use in non-parametric regression. Using tools from optimal transport, calculus of variations, and analysis of PDEs, I will discuss a series of results establishing the asymptotic consistency (with rates of convergence) of many of these analytical objects, as well as provide some perspectives on future research directions.

• Speaker: Leonardo Abbrescia, MSU
• Title: Moser iteration for parabolic equations
• Date: 02/18/2019
• Time: 1:40 PM - 3:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Paul Dawkins, Northern Illinois University
• Title: The use(s) of “is” in Mathematics
• Date: 02/19/2019
• Time: 2:00 PM - 3:30 PM
• Place: 252 EH

This talk presents analysis of some of the ambiguities that arise among statements with the copular verb “is" in the mathematical language of textbooks as compared to day-to-day English language. We identify patterns in the construction and meaning of is statements using randomly selected examples from corpora representing the two linguistic registers. We categorize these examples according to the part of speech of the object word in the grammatical form “[subject] is [object].” In each such grammatical category, we compare the relative frequencies of the subcategories of logical relations conveyed by that construction. Within some categories we observe that the same grammatical structure alternatively conveys different logical relations and that the intended logical relation can only sometimes be inferred from the grammatical cues in the statement itself. This means that one can only interpret the intended logical relation by already knowing the relation among the semantic categories in question. Such ambiguity clearly poses a communicative challenge for teachers and students. We discuss the pedagogical significance of these patterns in mathematical language and consider the relationship between these patterns and mathematical practices.

• Speaker: Ilya Gekhtman , University of Toronto
• Title: Growth rates of invariant random subgroups of hyperbolic groups and rank 1 Lie groups.
• Date: 02/21/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

Abstract: Invariant random subgroups (IRS) are conjugacy invariant probability measures on the space of subgroups of a given group G. They arise naturally as point stabilizers of probability measure preserving actions. The space of invariant random subgroups of SL_{2}R can be regarded as a natural compactification of the moduli space of Riemann surfaces, related to the Deligne-Mumford compactification. Invariant random subgroups can be regarded as a generalization both of normal subgroups and of lattices in topological groups. As such, it is interesting to extend results from the theories of normal subgroups and of lattices to the IRS setting. Jointly with Arie Levit, we prove such a result: the critical exponent (exponential growth rate) of an infinite IRS in an isometry group of a Gromov hyperbolic space (such as a rank 1 Lie group, or a hyperbolic group) is almost surely greater than half the Hausdorff dimension of the boundary. This generalizes an analogous result of Matsuzaki-Yabuki-Jaerisch for normal s As a corollary, we obtain that if $\Gamma$ is a typical subgroup and $X$ a rank 1 symmetric space then $\lambda_{0}(X/\Gamma)<\lambda_{0}(X)$ where $\lambda_0$ is the bottom of the spectrum of the Laplacian. The proof uses ergodic theorems for actions of hyperbolic groups. I will also talk about results about growth rates of normal subgroups of hyperbolic groups that inspired this work.

• Speaker: Alex Waldron, MSU
• Title: Twisted harmonic maps and the self-duality equations
• Date: 02/25/2019
• Time: 1:40 PM - 2:50 PM
• Place: C517 Wells Hall

I will describe Donaldson's 1986 paper with the same title.

• Speaker: Round Table Discussion
• Title: Pros and Cons for Evening Exams for Uniform Courses
• Date: 02/25/2019
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall

No abstract available.

• Speaker: Eva Belmont, Northwestern University
• Title: Localizing the E_2 page of the Adams spectral sequence
• Date: 02/28/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

The Adams spectral sequence is one of the central tools for calculating the stable homotopy groups of spheres, one of the motivating problems in stable homotopy theory. This talk focuses on the E_2 page, which can be calculated algorithmically in a finite range but whose large-scale structure is too complicated to be understood in full. I will give an introduction to some features of the Adams E_2 page for the sphere at p = 3, and discuss an approach for calculating it in an infinite region. This approach relies on computing an analogue of the Adams spectral sequence in Palmieri's stable category of comodules, which can be regarded as an algebraic analogue of stable homotopy theory.

• Speaker: Ikpe Dennis, MSU
• Title: A Levy Regime-Switching Temperature Dynamics Model for Weather Derivatives
• Date: 02/28/2019
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall

Linked Abstract

• Speaker: Gorapada Bera
• Title: Taubes' approach to the Casson invariant: an overview
• Date: 03/11/2019
• Time: 1:40 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Huyi Hu, MSU
• Title: The essential coexistence phenomenon in Hamiltonian dynamics
• Date: 03/12/2019
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

We construct an example of a Hamiltonian flow $f^t$ on a $4$-dimensional smooth manifold $\mathcal{M}$ which after being restricted to an energy surface $\mathcal{M}_e$ demonstrates essential coexistence of regular and chaotic dynamics, that is, there is an open and dense $f^t$-invariant subset $U\subset\mathcal{M}_e$ such that the restriction $f^t|U$ has non-zero Lyapunov exponents in all directions (except the direction of the flow) and is a Bernoulli flow while on the boundary $\partial U$, which has positive volume, all Lyapunov exponents of the system are zero. This is a continuation of the talk in previous week.

• Speaker: Yusuf Mustopa, UMass Amherst/Tufts University
• Title: Effective Global Generation on Varieties with Numerically Trivial Canonical Bundle
• Date: 03/13/2019
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

Fujita’s freeness conjecture predicts that if X is a smooth projective variety and A is an ample divisor on X, then K+mA is basepoint-free when m is at least dim(X)+1. Although this statement is optimal (as can be seen when X is projective space) there are much better statements for abelian varieties and surfaces with numerically trivial canonical bundle. In this talk, I will discuss a result of Fujita type for smooth projective varieties having numerically trivial canonical bundle, as well as its application to moduli spaces of sheaves on abelian surfaces. This is joint work with Alex Kuronya.

• Speaker: Jonas Lührmann, Johns Hopkins
• Title: Local smoothing estimates for Schrödinger equations on hyperbolic space and applications
• Date: 03/13/2019
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

We establish frequency-localized local smoothing estimates for Schrödinger equations on hyperbolic space. The proof is based on the positive commutator method and a heat flow based Littlewood-Paley theory. Our results and techniques are motivated by applications to the problem of stability of solitary waves to nonlinear Schrödinger-type equations on hyperbolic space. The talk is based on joint work with Andrew Lawrie, Sung-Jin Oh, and Sohrab Shahshahani.

• Speaker: AMS Student Chapter, MSU
• Title: Math trivia night
• Date: 03/14/2019
• Time: 5:30 PM - 7:30 PM
• Place: C204 Wells Hall

The AMS Student Chapter is hosting a math trivia night on pi day! Please join us for a potluck and a lot of fun.

• Speaker: Wenzhao Chen, MSU
• Title: Casson's invariant for oriented integer homology spheres
• Date: 03/18/2019
• Time: 1:40 PM - 3:00 PM
• Place: C304 Wells Hall

This talk is an exposition of Casson's invariant: we will cover the definition of Casson's invariant in terms of Heegaard decomposition and representation spaces, and show how it can be computed (and defined) in terms of the Alexander polynomial of knots.

• Speaker: Brent Nelson, Vanderbilt and MSU
• Title: Free Stein Information
• Date: 03/19/2019
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall

Given a von Neumann algebra M equipped with a trace, any self-adjoint operator in M can be thought of as a non-commutative random variable. For an n-tuple X of such operators, the free Stein information of X is a free probabilistic quantity defined by the behavior of a non-commutative Jacobian on the polynomial algebra generated by entries of X. It is a number in the interval [0,n] and its value can provide information about the entries of X as well as the von Neumann algebra they generate. In this talk, I will discuss these and other properties of the free Stein information and consider a few examples where it can be explicitly computed. This is based on joint work with Ian Charlesworth.

• Speaker: Shlomo Levental, MSU
• Title: Poincare type inequalities via 1-dimensional Malliavin calculus
• Date: 03/21/2019
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall

We will review briefly 3 types of operators which are mapping spaces of real-valued functions which are defined on the real line equipped with standard normal probability measure. Those are the derivative, divergence and Ornstein-Uklenbeck operators. There are simple formulas that describe the relationships between those operators. Using those formulas the proofs of the following will be presented: 1. Poincare inequality : The variance of a function of N(0,1) is dominated by the second moment of its derivative. 2. An upper bound to the Wasserstein distance between the distribution of a function of N(0,1) (the function has mean 0 and standard deviation 1) and N(0,1) itself. This upper bound is (up to a constant) the multiplication of the L4 norm of the function derivative and the L4 norm of the function 2nd derivative. The material is based on Nourdin and Peccati book.

• Speaker: Wilfrid Gangbo, University of California, Los Angeles
• Title: A weaker notion of convexity for Lagrangians not depending solely on velocities and positions
• Date: 03/21/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

In dynamical systems, one often encounters actions $\mathcal{A}\equiv \int_{\Omega}L(x, v(x))\rho dx$ which depend only on $v$, the velocity of the system and on $\rho$ the distribution of the particles. In this case, it is well–understood that convexity of $L(x, \cdot)$ is the right notion to study variational problems. In this talk, we consider a weaker notion of convexity which seems appropriate when the action depends on other quantities such as electro–magnetic fields. Thanks to the introduction of a gauge, we will argue why our problem reduces to understanding the relaxation of a functional defined on the set of differential forms (Joint work with B. Dacorogna).

• Speaker: Paul Irving and Daryl McPadden , Physics, MSU
• Title: Group based assessments
• Date: 03/25/2019
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall

No abstract available.

• Speaker: Yash Jhaveri, Institute for Advanced Study
• Title: Higher Regularity of the Singular Set in the Thin Obstacle Problem
• Date: 03/27/2019
• Time: 4:10 PM - 5:00 PM
• Place: C517 Wells Hall

In this talk, I will give an overview of some of what is known about solutions to the thin obstacle problem, and then move on to a discussion of a higher regularity result on the singular part of the free boundary. This is joint work with Xavier Fernández-Real.

• Speaker: Daping Weng, MSU
• Title: Cluster Structures on Double Bott-Samelson Cells
• Date: 03/28/2019
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall

Let $G$ be a Kac-Peterson group associated to a symmetrizable generalized Cartan matrix. Let $(b, d)$ be a pair of positive braids associated to the root system. We define the double Bott-Samelson cell associated to $G$ and $(b,d)$ to be the moduli space of configurations of flags satisfying certain relative position conditions. We prove that they are affine varieties and their coordinate rings are upper cluster algebras. We construct the Donaldson-Thomas transformation on double Bott-Samelson cells and show that it is a cluster transformation. In the cases where $G$ is semisimple and the positive braid $(b,d)$ satisfies a certain condition, we prove a periodicity result of the Donaldson-Thomas transformation, and as an application of our periodicity result, we obtain a new geometric proof of Zamolodchikov's periodicity conjecture in the cases of $D\otimes A_n$. This is joint work with Linhui Shen.

• Speaker: Ken Ono, Emory University
• Title: Jensen–Polya Program for the Riemann Hypothesis and Related Problems
• Date: 03/28/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity had only been proved for degrees $d=1,2,3$. We prove the hyperbolicity of all (but possibly finitely many) the Jensen polynomials of every degree $d$. Moreover, we establish the outright hyperbolicity for all degrees $d< 10^{26}$. These results follow from an unconditional proof of the "derivative aspect" GUE distribution for zeros. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.

• Speaker: Ken Ono, Emory University
• Title: Distinguished Undergraduate Lecture: Why Does Ramanujan, “The Man Who Knew Infinity,” Matter?
• Date: 03/29/2019
• Time: 4:10 PM - 5:00 PM
• Place: B119 Wells Hall

Srinivasa Ramanujan, one of the most inspirational figures in the history of mathematics, was a poor gifted mathematician from lush south India who left behind three notebooks that engineers, mathematicians, and physicists continue to mine today. Born in 1887, Ramanujan was a two-time college dropout. He could have easily been lost to the world, a thought that scientists cannot begin to absorb. He died in 1920. Prof. Ono will explain why Ramanujan matters today, and will share several clips from the film, “The Man Who Knew Infinity,” starring Dev Patel and Jeremy Irons. Professor Ono served as an associate producer and mathematical consultant for the film. Bio: Ken Ono is the Asa Griggs Candler Professor of Mathematics at Emory University and the Vice President of the American Mathematical Society. He is considered to be an expert in the theory of integer partitions and modular forms. He has been invited to speak to audiences all over North America, Asia and Europe. His contributions include several monographs and over 170 research and popular articles in number theory, combinatorics and algebra. He received his Ph.D. from UCLA and has received many awards for his research in number theory, including a Guggenheim Fellowship, a Packard Fellowship and a Sloan Fellowship. He was awarded a Presidential Early Career Award for Science and Engineering (PECASE) by Bill Clinton in 2000 and he was named the National Science Foundation’s Distinguished Teaching Scholar in 2005. In addition to being a thesis advisor and postdoctoral mentor, he has also mentored dozens of undergraduates and high school students. He serves as Editor-in-Chief for several journals and is an editor of The Ramanujan Journal. He was also an associate producer of the 2016 Hollywood film “The Man Who Knew Infinity” which starred Jeremy Irons and Dev Patel.

• Speaker: Nick Rekuski, MSU
• Title: Minimal Free Resolutions
• Date: 04/01/2019
• Time: 3:00 PM - 4:00 PM
• Place: C517 Wells Hall

The Hilbert function is a classical invariant of a variety (with a given embedding) that is easy to compute. It determines some properties of the variety (such as degree, dimension, and arithmetic genus), but it cannot determine more sophisticated invariants. A minimal free resolution determines more sophisticated properties of the variety while still being easily computable. For example, any set of seven points in P^3 in linearly general position has the same Hilbert function, but minimal free resolutions can distinguish whether the points lie on a rational normal curve. Furthermore, a minimal free resolution retains all the information of the Hilbert function. In this talk, we will define a minimal free resolution and associated invariants. With the definitions in place, we will show that minimal free resolutions retain all the information of the Hilbert function then explain the above example. If time permits, we will additionally show that minimal free resolutions are well behaved when restricting a variety to a hypersurface.

• Speaker: John Machacek, York University
• Title: Sign variation and boundary measurement in projective space
• Date: 04/04/2019
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall

We are interested in the topology of some spaces obtained by relaxing total positivity in the real Grassmannian. We define two families of subsets of the Grassmannian each of which include both the totally nonnegative Grassmannian and the whole Grassmannian. In this initial study of such subsets of the Grassmannian we focus of subsets of real projective space where interesting topology already appears. We we are able to find a regular CW complex which can be leveraged to compute some invariants like the fundamental group and Euler characteristic. We also conjecture some "ball-like" properties (e.g. Cohen-Macualayness).

• Speaker: Guang Lin, Purdue University
• Title: Uncertainty Quantification and Machine Learning of the Physical Laws Hidden Behind the Noisy Data
• Date: 04/05/2019
• Time: 4:10 PM - 5:00 PM
• Place: 1502 Engineering Building

In this talk, I will present a new data-driven paradigm on how to quantify the structural uncertainty (model-form uncertainty) and learn the physical laws hidden behind the noisy data in the complex systems governed by partial differential equations. The key idea is to identify the terms in the underlying equations and to approximate the coefficients of the terms with error bars using Bayesian machine learning algorithms on the available noisy measurement. In particular, Bayesian sparse feature selection and parameter estimation are performed. Numerical experiments show the robustness of the learning algorithms with respect to noisy data and size, and its ability to learn various candidate equations with error bars to represent the quantified uncertainty.

• Speaker: Mona Merling, University of Pennsylvania
• Title: The equivariant stable parametrized h-cobordism theorem
• Date: 04/08/2019
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

The stable parametrized h-cobordism theorem provides a critical link in the chain of homotopy theoretic constructions that show up in the classification of manifolds and their diffeomorphisms. For a compact smooth manifold M it gives a decomposition of Waldhausen's A(M) into QM_+ and a delooping of the stable h-cobordism space of M. I will talk about joint work with Malkiewich on this story when M is a smooth compact G-manifold.

• Speaker: Joe Melby
• Title: Knot Genus and Complexity
• Date: 04/10/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

A classical problem in knot theory is determining whether or not a given 2-dimensional diagram represents the unknot. The UNKNOTTING PROBLEM was proven to be in NP by Hass, Lagarias, and Pippenger. A generalization of this decision problem is the GENUS PROBLEM. ​We will discuss the basics of computational complexity, knot genus, and normal surface theory in order to present an algorithm (from HLP) to explicitly compute the genus of a knot. We will then show that this algorithm is in PSPACE and discuss more recent results and implications in the field.

• Speaker: Nick Rekuski, MSU
• Title: Fargues-Fontaine Curve: Part I
• Date: 04/12/2019
• Time: 2:00 PM - 4:00 PM
• Place: C204A Wells Hall

There is a close analogy between function fields over finite fields and number fields. In this analogy $\text{Spec } \mathbb{Z}$ corresponds to an algebraic curve over a finite field. However, this analogy often fails. For example, $\text{Spec } \mathbb{Z} \times \text{Spec } \mathbb{Z} $ (which should correspond to a surface) is $\text{Spec } \mathbb{Z}$ (which corresponds to a curve). In many cases, the Fargues-Fontaine curve is the natural analogue for algebraic curves. In this first talk, we will give the construction of the Fargues-Fontaine curve.

• Speaker: Tom Parker, MSU
• Title: A short proof of the Gromov Convergence theorem for J-holomorphic maps
• Date: 04/15/2019
• Time: 1:45 PM - 3:00 PM
• Place: C517 Wells Hall

No abstract available.

• Speaker: Gorapada Bera
• Title: Introduction to Seiberg Witten invariants on three manifolds
• Date: 04/17/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Although Seiberg Witten invariant originally introduced for four manifolds, but its three dimensional version is also interesting .After a brief discussion on the definition of the Seiberg Witten invariant on three manifolds we will see some results from literature equating this invariant to some known invariants of three manifolds.

• Speaker: Nick Rekuski, MSU
• Title: Fargues-Fontaine Curve: Part II
• Date: 04/19/2019
• Time: 2:00 PM - 4:00 PM
• Place: C204A Wells Hall

No abstract available.

• Speaker: Jane Zimmerman, MSU
• Title: MTH 103A/B: Experiences from the classroom and future directions
• Date: 04/22/2019
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall

No abstract available.

• Speaker: André Neves, University of Chicago
• Title: TBA
• Date: 04/25/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.