• Speaker: 
• Title: Organizational meeting
• Date: 09/03/2019
• Time: 12:00 PM - 1:30 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Ramis Movassagh, IBM
• Title: Proof of average-case #P- hardness of random circuit sampling with some robustness, and a protocol for blind quantum computation
• Date: 09/05/2019
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall

A one-parameter unitary-valued interpolation between any two unitary matrices (e.g., quantum gates) is constructed based on the Cayley transformation. We prove that this path induces probability measures that are arbitrarily close to the Haar measure and prove the simplest known average-case # P -hardness of random circuit sampling (RCS). RCS is the task of sampling from the output distribution of a quantum circuit whose local gates are random Haar unitaries, and is the lead candidate for demonstrating quantum supremacy in the "noisy intermediate scale quantum (NISQ)" computing era. Here we also prove exp(-Θ(n^4 )) robustness with respect to additive error. This overcomes issues that arise for extrapolations based on the truncations of the power series representation of the exponential function. (Dis)Proving the quantum supremacy conjecture requires an extension of this analysis to noise that is polynomially small in the system's size. This remains an open problem. Lastly, an efficient and private protocol for blind quantum computation is proposed that uses the Cayley deformations proposed herein for encryption. This is an efficient protocol that only requires classical communication between Alice and Bob. ** The talk is self-contained and does not require any pre-req beyond basic linear algebra (e.g, knowing what a unitary matrix is).

• Speaker: Erik Bates, UC Berkeley
• Title: Localization of Gaussian disordered systems at low temperature
• Date: 09/05/2019
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall

The fundamental premise of statistical mechanics is that a physical system's state is random according to some probability measure, which is determined by the various forces of interaction between the system's constituent particles. In the ``disordered" setting, these interactions are also random (meant to capture the effect of a random medium), meaning the probability measure is itself a random object. This setting includes several of the models most widely studied by mathematical physicists, such as the Random Energy Model, the Sherrington--Kirkpatrick spin glass, and directed polymers. The most intriguing part of their phase diagrams occurs at low temperature, when the measure concentrates, or "freezes", on energetically favorable states. In general, quantifying this phenomenon is especially challenging, in large part due to the extra layer of randomness created by the disorder. This talk will describe recent progress on this question, leading us to some conjectures on further open problems. (Joint work with Sourav Chatterjee)

• Speaker: AMS Student Chapter, MSU
• Title: Potluck and introduction
• Date: 09/09/2019
• Time: 4:00 PM - 5:00 PM
• Place: C204 Wells Hall

Come learn what AMS is all about, what events are scheduled for this year, and meet your student community! This event is for ALL members, new and returning. We'd love it if you could bring a snack or dish to share if you're able to. We are also looking to fill two eboard positions: secretary and treasurer! We will discuss more about these positions on Tuesday and would love to hear from you if you're interested.

• Speaker: Ioannis Zachos, Michigan State
• Title: Gröbner basis and the Ideal Membership problem
• Date: 09/09/2019
• Time: 4:30 PM - 5:30 PM
• Place: C304 Wells Hall

We know from the Hilbert Basis Theorem that any ideal in a polynomial ring over a field is finitely generated. However, there remains question as to the best generators to choose to describe the ideal. Are there generators for a polynomial ideal $I$ that make it easy to see if a given polynomial $f$ belongs to $I$? For instance, does $2x^2z^2+2xyz^2+2xz^3+z^3-1$ belong to $I=(x+y+z, xy+xz+yz, xyz−1)$? Deciding if a polynomial is in an ideal is called the Ideal Membership Problem. In polynomial rings of one variable, we use long division of polynomials to solve this problem. There is a corresponding algorithm for $K[x_1,\ldots, x_n]$, but because there are multiple variables and multiple divisors, the remainder of the division is not unique. Hence a remainder of $0$ is a sufficient condition, but not a necessary condition, to determine ideal membership. However, if we choose the correct divisors, then the remainder is unique regardless of the order of the divisors. These divisors are called a Gröbner basis. In our talk we will define the Gröbner basis and see how it solves the Ideal Membership Problem.

• Speaker: Bruce Sagan, MSU
• Title: Combinatorial interpretations of Lucas analogues
• Date: 09/11/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

The Lucas sequence is a sequence of polynomials in $s,t$ defined recursively by $\{0\}=0$, $\{1\}=1$, and $\{n\}=s\{n-1\}+t\{n-2\}$ for $n\ge2$. On specialization of $s$ and $t$ one can recover the Fibonacci numbers, the nonnegative integers, and the $q$-integers $[n]_q$. Given a quantity which is expressed in terms of products and quotients of nonnegative integers, one obtains a Lucas analogue by replacing each factor of $n$ in the expression with $\{n\}$. It is then natural to ask if the resulting rational function is actually a polynomial in $s$ and $t$ and, if so, what it counts. Using lattice paths, we give combinatorial models for Lucas analogues of binomial coefficients. We also consider Catalan numbers and their relatives, such as those for finite Coxeter groups. This is joint work with Curtis Bennett, Juan Carrillo, and John Machacek.

• Speaker: Mike Hartglass, Santa Clara University
• Title: Free products of finite-dimensional von Neumann algebras
• Date: 09/12/2019
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall

I will present joint work with Brent Nelson, where we classify the structure of free products of von Neumann algebras equipped with arbitrary states. Our techniques use our other joint work of assigning a von Neumann algebra associated to a weighted graph. I will discuss this work and how it leads to computing finite-dimensional free products.

• Speaker: Jiangguo (James) Liu, Colorado State University
• Title: Developing Finite Element Solvers for Poroelasticity in the Two-field Approach
• Date: 09/13/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

This talk presents results from our recent efforts for reviving the 2-field approach (fluid pressure and solid displacement) for numerically solving poroelasticity problems. We choose quadrilateral and hexahedral meshes for spatial discretization since they are equally flexible in accommodating complicated domain geometry but involve less unknowns, compared to simplicial meshes. The Darcy equation is solved for fluid pressure by the novel weak Galerkin finite element methods, which establish the discrete weak gradient and numerical velocity in the Arbogast-Correa spaces. The elasticity equation is solved for solid displacement by the enriched Lagrangian elements, which were motivated by the Bernardi-Raugel elements for Stokes flow. These two types of finite elements are coupled through the implicit Euler temporal discretization to solve poroelasticity. Numerical experiments on benchmarks will be presented to show that the new solvers are locking-free. Implementation on deal.II will be discussed also. This talk is based on a series of joint work with several collaborators.

• Speaker: Dongsoo Lee, MSU
• Title: Morse homology
• Date: 09/17/2019
• Time: 12:00 PM - 1:00 PM
• Place: C304 Wells Hall

First meeting of seminar on instanton Floer homology.

• Speaker: Nick Rekuski, MSU
• Title: Perfectoid Fields and Tilting
• Date: 09/19/2019
• Time: 10:00 AM - 11:30 AM
• Place: C329 Wells Hall

In this talk we will introduce perfectoid fields and tilting. Perfectoid fields provide the the correct base scheme for perfectoid spaces. Tilting is a fundamental tool that will let us lift characteristic $0$ results to characteristic $p$ results. For example, if $K$ is a characteristic $0$ perfectoid field and $K^{\flat}$ is a tilt of $K$ then $K^{\flat}$ is a characteristic $p$ field; $K^{\circ}/K^{\circ\circ}\cong K^{\flat \circ}/K^{\flat\circ\circ}$; if $[L:K]$ is finite then $[L^{\flat}:K^{\flat}]=[L:K]$ (in particular, $L$ is perfectoid); and there is an equivalence of categories between finite étale covers of $K$ and finite étale covers of $K^{\flat}$ via $L\mapsto L^{\flat}$. This talk will not require any material beyond first-year graduate algebra. However, the sophistication required may be higher. To make this talk as accessible as possible, we will include numerous examples.

• Speaker: Aaron Naber, Northwestern University
• Title: Introduction to the Energy Identity for Yang-Mills
• Date: 09/19/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

In this talk we give an introduction to the analysis of the Yang-Mills equation in higher dimensions. In particular, when studying sequences of solutions we will study the manner in which blow up can occur, and how this blow up may be understood through the classical notions of the defect measure and bubbles. The energy identity is an explicit conjectural relationship relating the energy density of the defect measure at a point to the bubbles which occur at that point. This talk is introductory and we will spend most of our time understanding the words of this abstract. If time permits we will briefly discuss the ideas needed to prove this conjecture and the related $W^{2,1}$-conjecture. The work is joint with Daniele Valtorta.

• Speaker: Nick Rekuski, Michigan State
• Title: Splitting Criteria for Vector Bundles on $\mathbb{P}^n$
• Date: 09/23/2019
• Time: 4:30 PM - 5:30 PM
• Place: C304 Wells Hall

Grothendieck's Theorem says that any vector bundle on $\mathbb{P}^1$ can be decomposed as a finite sum of line bundles. In this talk, we will discuss a generalization of this theorem: Horrocks Splitting Criterion. This criterion completely describes when a vector bundle on $\mathbb{P}^n$ splits as a sum of line bundles. We will then discuss an open conjecture of Hartshorne. If time permits, we will also consider the similar question of classifying when a vector bundle on $\mathbb{P}^n$ decompose as line bundles and twists of the tangent bundle.

• Speaker: Honghao Gao, MSU
• Title: Legendrian knots and augmentation varieties
• Date: 09/24/2019
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall

We begin with a gentle introduction to Legendrian knot and its invariant theory. We will define the Chekanov-Eliashberg different graded algebra and augmentations associated to the dga. We also present an example where the augmentation variety is a cluster variety.

• Speaker: Chuangtian Guan, MSU
• Title: Almost Mathematics
• Date: 09/26/2019
• Time: 10:00 AM - 12:00 PM
• Place: C329 Wells Hall

No abstract available.

• Speaker: A. Volberg/P. Mozolyako
• Title: Unexpected combinatorial properties of all planar measures
• Date: 09/26/2019
• Time: 1:00 PM - 1:50 PM
• Place: C517 Wells Hall

We will start with paraproducts--operators used in PDE to prove Leibniz rule with fractional derivatives. Then we move to bi-parameter paraproducts and prove the property from the title.

• Speaker: Keshav Sutrave, MSU
• Title: Some kind of introduction to special relativity
• Date: 09/30/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

(Soft) The beginning of Einstein's theory of special relativity, which gives us a way of doing physics in different reference frames (observers in motion). Specifically: "What happens when you turn on a flashlight while already moving at half the speed of light?" I will introduce time dilation and length contraction, event simultaneity, and touch on the problem in electromagnetism, using many examples.

• Speaker: Keshav Sutrave, MSU
• Title: Chern-Simons functional as a Morse function
• Date: 10/01/2019
• Time: 12:00 PM - 1:30 PM
• Place: C117 Wells Hall

No abstract available.

• Speaker: Victoria Hand , University of Colorado, Boulder; Elizabeth Mendoza, University of California, Irvine; Justin TenEyck, “I have a Dream” Foundation of Boulder County
• Title: Toward Re-humanizing Mathematics Education: Participatory Approaches to Noticing in Mathematics Classrooms
• Date: 10/02/2019
• Time: 3:00 PM - 4:30 PM
• Place: 252 EH

Researchers are increasingly calling for participatory approaches to educational research that center the voices, experiences, and participation of minoritized communities. This talk will report on the Co-Attend research project, which is grounded in a participatory approach to mathematics teacher noticing. The project involves mathematics teachers, leaders of local community-based organizations and university researchers in collectively understanding expansive, multisensory noticing that supports re-humanizing practices in mathematics classrooms. All participants are positioned as researchers and co-analyze project data in video club meetings and summer institutes. We will describe emerging findings from the project, both in terms of the noticing framework, as well as the participatory process.

• Speaker: Rita Gitik, Michigan
• Title: On Geodesic Triangles in the Hyperbolic Plane
• Date: 10/03/2019
• Time: 2:00 PM - 2:50 PM
• Place: C304 Wells Hall

Let M be an orientable hyperbolic surface without boundary and let c be a closed geodesic in M. We prove that any side of any triangle formed by distinct lifts of c in the hyperbolic plane is shorter than c. The talk will be presented for advanced undergraduate and beginning graduate students.

• Speaker: Zheng Xiao, MSU
• Title: Recent results of GCD problems on almost $S$-units and recurrences
• Date: 10/07/2019
• Time: 4:30 PM - 5:30 PM
• Place: C517 Wells Hall

The GCD problem is one of the major problems in Diophantine Geometry. Corvaja, Zannier and Bugeaud first gave a fundamental result on GCD of integers powers and then generalized to rational numbers and algebraic numbers by many mathematicians. In this talk I will introduce recent GCD results on $S$-units due to Levin and generalize to almost $S$-units. I will give the definition of almost units and present the main theorem of GCD on multivariable polynomials, which is lead to a result about recurrence sequences. If time allows, I will also introduce Silverman’s generalized GCD along the blow up of a closed subscheme and apply to abelian surface case and its connection to Vojta’s conjecture.

• Speaker: Daping Weng, MSU
• Title: Double Bott-Samelson cell and the moduli space of microlocal rank-1 sheaves
• Date: 10/08/2019
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall

Shende, Treumann, and Zaslow gave a combinatorial description of the moduli space of microlocal rank-1 sheaves in their paper “Legendrian Knots and Constructible sheaves”. Following a result of Guillermou, Kashiwara, and Schapira, this moduli space is an invariant of Legendrian links. In this talk, I will review the definition and the cluster structure on the (undecorated) double Bott-Samelson cells, and show that in the cases of positive braids of Dynkin type A_r, the undecorated double Bott-Samelson cells are isomorphic to moduli spaces of microlocal rank-1 sheaves associated to the corresponding braid closures. As a corollary, the undecorated double Bott-Samelson cells of Dynkin type A_r are also Legendrian link invariants for positive braid closures. If time allows, I will also talk about how to count F_q points on the undecorated double Bott-Samelson cells.

• Speaker: Jeffrey Schenker, Michigan State University
• Title: An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states
• Date: 10/10/2019
• Time: 11:30 AM - 12:30 PM
• Place: C304 Wells Hall

Quantum channels represent the most general physical evolution of a quantum system through unitary evolution and a measurement process. Mathematically, a quantum channel is a completely positive and trace preserving linear map on the space of $D\times D$ matrices. We consider ergodic sequences of channels, obtained by sampling channel valued maps along the trajectories of an ergodic dynamical system. The repeated composition of these maps along such a sequence could represent the result of repeated application of a given quantum channel subject to arbitrary correlated noise. It is physically natural to assume that such repeated compositions are eventually strictly positive, since this is true whenever any amount of decoherence is present in the quantum evolution. Under such an hypothesis, we obtain a general ergodic theorem showing that the composition of maps converges exponentially fast to a rank-one -- “entanglement breaking’’ – channel. We apply this result to describe the thermodynamic limit of ergodic matrix product states and prove that correlations of observables in such states decay exponentially in the bulk. (Joint work with Ramis Movassagh)

• Speaker: Romyar Sharifi, UCLA
• Title: Modular symbols and the arithmetic of cyclotomic fields
• Date: 10/10/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

The arithmetic of cyclotomic fields, and the structure of their class groups, has been studied since the time of Kummer in connection with Fermat’s Last Theorem. The work of Ribet in 1976 uncovered a subtle influence of the geometry of modular curves on this structure. I’ll discuss how this connection goes even deeper and define a surprisingly explicit map from the homology group of a modular curve to a K-group related to the class group of a cyclotomic field. I’ll then indicate how this is turning out to be just one instance of a more general phenomenon, touching briefly on joint work with Takako Fukaya and Kazuya Kato and separate joint work with Akshay Venkatesh.

• Speaker: Zhe Zhang, MSU
• Title: An introduction to intersection forms: Taking K3 surface as an example
• Date: 10/14/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

I’ll define intersection product both on 4 manifolds and in the algebraic geometry setting, then introduce the blow up technique and give some easy examples. After that I will jump to K3 surface, give definition and constructions, and talk a little bit about the elliptic fibrations of K3. If I still have time, I will talk about the relation between intersection form and characteristic classes.

• Speaker: Wenchuan Tian, MSU
• Title: Linear analysis on cylindrical-end manifolds
• Date: 10/15/2019
• Time: 12:00 PM - 1:30 PM
• Place: C117 Wells Hall

Donaldson Ch. 3

• Speaker: Aklilu Zeleke, MSU
• Title: New and Old Combinatorial Identities Part I
• Date: 10/16/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

Binomial coefficients $n \choose k$ appear in different areas of mathematics (in Pascal's triangle, counting problems and computing probabilities to name few). There are also many identities that involve binomial coefficients. In this talk we will discuss new and old identities that represent positive integers and in some cases real numbers. These identities are derived from studying the asymptotic behavior of the roots of a generalized Fibonacci polynomial sequence given by $F_{j}(x)=x^{j}-...-x-1$.

• Speaker: Frank Sottile, Texas A&M University
• Title: Higher convexity for complements of tropical objects
• Date: 10/17/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Gromov generalized the notion of convexity for open subsets of $\mathbf{R}^n$ with hypersurface boundary, defining $k$-convexity, or higher convexity and Henriques applied the same notion to complements of amoebas. He conjectured that the complement of an amoeba of a variety of codimension $k+1$ is $k$-convex. I will discuss work with Mounir Nisse in which we study the higher convexity of complements of coamoebas and of tropical varieties, proving Henriques' conjecture for coamoebas and establishing a form of Henriques' conjecture for tropical varieties in some cases.

• Speaker: Jack Smith, MSU; Shiv Karunakaran, MSU
• Title: When the Game Changes: The Development of Student Agency and Autonomy in Challenging Undergraduate Mathematics
• Date: 10/21/2019
• Time: 12:00 PM - 1:00 PM
• Place: 115 Erickson Hall

In their pre-college and introductory collegiate mathematics coursework, students learn that mathematics centrally, if not exclusively involves computation. But many who pursue STEM disciplines routinely could encounter a quite different kind of mathematical work: The composition and evaluation of formal mathematical arguments, including proofs. The locus of this shift in mathematical activity on the MSU campus is MTH 299, Transitions, which introduces students to the basics of proof and argument. In the talk, we will present our current work conceptualizing agency and autonomy, the students who take the course, the challenges they face, and what we are learning about their experience in the course. We hope that these lessons will prove useful to all efforts to enrich introduction to proof mathematics courses.

• Speaker: Andy Krause, MSU
• Title: Instructional Faculty Observations and Evaluation
• Date: 10/21/2019
• Time: 4:10 PM - 5:00 PM
• Place: C109 Wells Hall

We'll revisit the Instructional Faculty observation structure (from our meeting in Spring) and organize classroom observations for the fall.

• Speaker: Gorapada Bera, MSU
• Title: Linear analysis on cylindrical-end manifolds (continued)
• Date: 10/22/2019
• Time: 12:00 PM - 1:30 PM
• Place: C117 Wells Hall

No abstract available.

• Speaker: Sumit Chandra Mishra, Emory University
• Title: Local-global principle for norms over semi-global fields
• Date: 10/23/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

Let $K$ be a complete discretely valued field with residue field $\kappa$. Let $F$ be a function field in one variable over $K$ and $\mathscr{X}$ a regular proper model of $F$ with reduced special fibre $X$ a union of regular curves with normal crossings. Suppose that the graph associated to $\mathscr{X}$ is a tree (e.g. $F = K(t)$). Let $L/F$ be a Galois extension of degree $n$ with Galois group $G$ and $n$ coprime to char$(\kappa)$. Suppose that $\kappa$ is algebraically closed field or a finite field containing a primitive $n^{\rm th}$ root of unity. Then we show that an element in $F^*$ is a norm from the extension $L/F$ if it is a norm from the extensions $L\otimes_F F_\nu/F_\nu$ for all discrete valuations $\nu$ of $F$.

• Speaker: Lev Tovstopyat-Nelip, MSU
• Title: Obstructing Lagrangian link cobordisms via Heegaard Floer homology.
• Date: 10/24/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

I'll explain how an invariant of Legendrian links in knot Floer homology can be used to obstruct the existence of decomposable Lagrangian link cobordisms in a very general setting. The argument involves braiding the ends of the cobordism about open books and appealing to an algebraic property of the Legendrian invariant called comultiplication. Much of the talk will be spent describing the topological and contact geometric ingredients.

• Speaker: Arman Tavakoli, MSU
• Title: Introduction to the Yang-Mills equation
• Date: 10/28/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

The Yang-Mills equation is a celebrated topic that is studied in differential geometry and particle physics. We will motivate the equation as a generalization of Maxwell's equations, define the relevant geometrical objects and discuss their properties.

• Speaker: Yu Shen, Michigan State
• Title: Serre Duality II
• Date: 10/28/2019
• Time: 4:30 PM - 5:30 PM
• Place: C517 Wells Hall

Serre duality was first proved by Serre in 1950s. It is a very useful tool in algebraic and complex geometry. In this lecture, I will use Čech cohomology to prove Serre duality of projective varieties. If time permits, I would like to talk about some applications of it.

• Speaker: Alexander Shapiro, UC Berkeley
• Title: Character varieties, Coulomb branches, and clusters.
• Date: 10/29/2019
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall

Quantum groups admit two different geometric realizations: as quantized character varieties and as quantized Coulomb branches of certain gauge theories. These realizations endow a quantum group with two, a priori different, cluster structures. In this talk I will show these structures, explain why they coincide, and say what they have to do with Gelfand-Tsetlin subalgebras, higher rank Fenchel–Nielsen coordinates, and modular functor from higher Teichmüller theory. This talk will be based on joint works with Gus Schrader.

• Speaker: Boyu Zhang, Princeton University
• Title: Classification of links with Khovanov homology of minimal rank
• Date: 10/31/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

In this talk, I will present a classification of links whose Khovanov homology has minimal rank, which answers a question asked by Batson and Seed. The proof is based on an excision formula for singular instanton Floer homology that allows the excision surface to intersect the singularity. We will use the excision theorem to define an instanton Floer homology for tangles on sutured manifolds, and show that its gradings detect the generalized Thurston norm for punctured surfaces. This is joint work with Yi Xie.

• Speaker: Victor Lie, Purdue University
• Title: A unified approach to three themes in harmonic analysis
• Date: 11/01/2019
• Time: 1:00 PM - 2:00 PM
• Place: C304 Wells Hall

Linked Abstract

• Speaker: Zheng Xiao, Michigan State
• Title: Arithmetic intersection theory and Arakelov's Hodge Index Theorem
• Date: 11/04/2019
• Time: 4:30 PM - 5:30 PM
• Place: C304 Wells Hall

The famous Mordell-Weil conjecture was first proved by Faltings in a classical way, then Vojta gave an alternative proof using arithmetic Arakelov geometry, which is one big motivation for developing Arakelov theory into a mature tool. In this talk I will introduce Neron functions and divisors, which is an arithmetic approach to define divisors rather than classical algebraic geometry. We shall also cover arithmetic chow groups and the arithmetic intersection number. In the end I will present Neron symbols and use it to give a sketch proof of Arakelov’s Hodge Index Theorem.

• Speaker: Carl Wang-Erickson, University of Pittsburg
• Title: Bi-ordinary modular forms
• Date: 11/05/2019
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

It is known that p-ordinary cuspidal Hecke eigenforms give rise to 2-dimensional global Galois representations which become reducible after restriction to a decomposition group at p. For which such forms is this restriction not only reducible but also splittable? Complex multiplication (CM) forms satisfy this p-local property, but is such a restrictive global property as CM necessary? In classical weights at least 2, it is expected that this is the case. We present a construction of "bi-ordinary" p-adic modular forms, which can measure exceptions to this expectation. We also give evidence that there are non-CM but p-locally splittable forms in p-adic weights. This is joint work with Francesc Castella.

• Speaker: Robert Bell, MSU
• Title: Variations of cops and robbers on infinite graphs
• Date: 11/06/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

The game of cops and robbers is a two player pursuit and evasion game played on a discrete graph G. We study a variation of the classical rules which leads to a different invariant when G is an infinite graph. In this variation, called "weak cops and robbers," the cops win by preventing the robber from visiting any vertex infinitely often. In the classical game, if G is connected and planar, then the cops can always win if there are at least three cops. We prove that this is true in the weak game if G is a locally finite plane graph with no vertex accumulation points.

• Speaker: Marios Velivasakis, University of Western Ontario
• Title: Schubert Varieties in Partial Flag Manifolds and Generalized Severi-Brauer Varieties
• Date: 11/07/2019
• Time: 11:00 AM - 12:00 PM
• Place: C329 Wells Hall

Schubert varieties form one of the most important classes of singular algebraic varieties. They are also a kind of moduli spaces. One problem is that these varieties are not easy to understand and manipulate using only their geometric nature. In this talk, we will discuss about Schubert varieties and present a way to characterize them combinatorially. In addition, we will discuss how they relate to Severi-Brauer varieties SB(d,A) and how we can use their combinatorial description to answer questions about subvarieties of SB(d,A)

• Speaker: Kritika Singhal, Ohio State University
• Title: Sketching and Clustering Metric Measure Spaces
• Date: 11/08/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Two important optimization problems in the analysis of geometric data sets are clustering and simplification (sketching) of data. Clustering refers to partitioning a dataset, according to some rule, into sets of smaller size with the aim of extracting important information from the data. Sketching, or simplification of data, refers to approximating the input data with another dataset of much smaller size in such a way that properties of the input dataset are retained by the smaller dataset. In this sense, sketching facilitates understanding of the data. There are many clustering methods for metric spaces (mm spaces) already present in literature, such as k-center clustering, k-median clustering, k-means clustering, etc. A natural method for obtaining a k-sketch of a metric space (mm space) is by viewing the space of all metric spaces (mm space) as a metric under Gromov-Hausdorff (Gromov-Wasserstein) distance, and then determining, under this distance, the k point metric space (mm space) closest to the input metric space (mm space). These two problems of sketching and clustering, a priori, look completely unrelated. However, we establish a duality i.e. an equivalence between these notions of sketching and clustering. For metric spaces, we consider the case where the clustering objective is minimizing the maximum cluster diameter. We show that the ratio between the sketching and clustering objectives is constant over compact metric spaces. We extend these results to the setting of metric measure spaces where we prove that the ratio of sketching to clustering objectives is bounded both above and below by some universal constants. In this setting, the clustering objective involves minimizing various notions of the $\ell_p$-diameters of the clusters. We also identify procedures/maps that transform a solution of the sketching problem to a solution of the clustering problem, and vice-versa. These maps give rise to algorithms for performing these transformations and, by virtue of these algorithms, we are able to obtain an approximation to the k-sketch of a metric measure space (metric space) using known approximation algorithms for the respective clustering objectives. This is joint work with Facundo Memoli and Anastasios Sidiropoulos, and is available online at https://arxiv.org/abs/1801.00551.

• Speaker: Wenchuan Tian, MSU
• Title: Properties of Busemann function on manifolds with nonnegative sectional curvature outside of a compact set
• Date: 11/11/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

Busemann functions are useful. Cheeger and Gromoll used them to prove the splitting theorem for manifolds with nonnegative ricci curvature that contains a line. Yau used them to prove that complete noncompact manifolds with nonnegative Ricci curvature have at least linear volume growth. In a paper called "Positive Harmonic Functions on Complete Manifolds with Non-Negative Curvature Outside a Compact Set" Peter Li and Luen-Fai Tam also used Busemann function to show the existence of positive harmonic functions. I will talk about Li and Tam's proof of properties of Busemann function. The proof only uses Toponogov theorem and cosine law. The results of the proof is useful for the subsequent analysis part of the paper.

• Speaker: Lev Tovstopyat, MSU
• Title: On the surgery exact triangle in Heegaard Floer homology
• Date: 11/12/2019
• Time: 12:00 PM - 1:30 PM
• Place: C117 Wells Hall

No abstract available.

• Speaker: Farhan Abedin, Michigan State University
• Title: Regularity results for a class of Kolmogorov-Fokker-Planck equations in non-divergence form
• Date: 11/13/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

The Kolmogorov-Fokker-Planck equation is a degenerate parabolic equation arising in models of gas dynamics from kinetic theory. The operator is of the form $$\mathcal{L}_Au := \mathrm{tr}(A(v,y,t) D^2_v u) + v \cdot \nabla_yu - \partial_tu,$$ where $$u(v,y,t): \mathbb{R}^{2d+1} \to \mathbb{R} \text{ and } 0 < \lambda \mathbb{I}_d \leq A \leq \Lambda \mathbb{I}_d.$$ It is an open problem if non-negative solutions of $\mathcal{L}_A u = 0$ in $\mathbb{R}^{2d+1}$ satisfy a scale-invariant Harnack inequality, assuming the matrix coefficient $A$ is merely bounded and measurable. I will discuss recent joint work with Giulio Tralli in which progress is made on partially solving this problem.

• Speaker: Jihye Hwang, Michigan State University
• Title: What do you mean by "show"? Is it the same as "prove"?
• Date: 11/14/2019
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall

Students face a mathematical task whenever they involve in doing mathematics. We wondered whether the word used in posing question impact students’ response and we hypothesize that task provider’s intention and students’ response can be different. This talk focus on students interpretation of the different prompts, such as “prove,” “show,” “explain,” and “convince a classmate,” for proving tasks. This talk focuses on the two prompts, “prove” and “show” as the prompts are regarded as synonymous by many people, especially mathematicians. Although there exist similarities between the prompts, the result mainly demonstrates students possibly have different meaning for “prove” and “show” depending on individual and one possible relationship between the two prompts.

• Speaker: Yao Yao, Georgia Tech
• Title: Uniqueness and non-uniqueness of steady states of aggregation-diffusion equation
• Date: 11/15/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

In this talk, I will discuss a nonlocal aggregation equation with degenerate diffusion, which describes the mean-field limit of interacting particles driven by nonlocal interactions and localized repulsion. When the interaction potential is attractive, it is previously known that all steady states must be radially decreasing up to a translation, but uniqueness (for a given mass) within this class was open, except for some special interaction potentials. For general attractive potentials, we show that the uniqueness/non-uniqueness criteria are determined by the power of the degenerate diffusion, with the critical power being m=2. Namely, for m>=2, we show the steady state for any given mass is unique for any attractive potential, by tracking the associated energy functional along a novel interpolation curve. And for 1<m<2, we construct examples of smooth attractive potentials, such that there are infinitely many radially decreasing steady states of the same mass. This is a joint work with Matias Delgadino and Xukai Yan.

• Speaker: Joshua Ruiter, Michigan State
• Title: Split and non-split tori
• Date: 11/18/2019
• Time: 4:30 PM - 5:30 PM
• Place: C517 Wells Hall

Tori are an important structural aspect of algebraic groups, and "split" vs "non-split" tori are especially important. Unfortunately, "non-split" phenomena only occur over non-algebraically closed fields, so not all the traditional tools of classical algebraic geometry apply. Using the generalized field norm map from my talk last week, I'll describe a concrete example of a non-split torus. Then we'll try to use that example to try and understand the importance of non-split tori.

• Speaker: Matthew Hedden, MSU
• Title: Spectral sequence from Khovanov to instanton homology
• Date: 11/19/2019
• Time: 12:00 PM - 1:30 PM
• Place: C117 Wells Hall

No abstract available.

• Speaker: Andrey Gogolyev, Ohio State University
• Title: Rigidity for higher dimensional expanding maps
• Date: 11/19/2019
• Time: 3:50 PM - 4:50 PM
• Place: C304 Wells Hall

Expanding maps are self covers of smooth compact manifolds which expand the lengths of all non-zero tangent vectors. Classification of such maps up to topological conjugacy is known due to work of Shub, Franks and Gromov. Classification up to smooth conjugacy should be quite different because periodic points of expanding maps carry invariants of $C^1$ conjugacy. Shub and Sullivan classified expanding maps on the circle up to smooth conjugacy on the circle. I will explain smooth classification of expanding maps in higher dimensions on and open dense set in the space of expanding maps. Joint work with F. Rodriguez Hertz.

• Speaker: Michelle Cirillo, University of Delaware; Jennifer Reed, Odyssey Charter Middle School, Delaware
• Title: Learning Together Through Collaborative Research: The Case of Proof in Secondary Mathematics
• Date: 11/20/2019
• Time: 3:30 PM - 5:00 PM
• Place: 252 EH

The Proof in Secondary Classrooms (PISC) project is a design and development research study focused on secondary students’ success with mathematical proof. The goal of this project was to develop a new and improved intervention to support the teaching and learning of proof. The central research objective of this project was to develop a pedagogical framework and a corresponding set of lesson plans and support materials to guide teachers toward improving students’ success with proof. The primary educational objective of this project was to support mathematics educators in understanding particular sub-goals of proof and developing strategies for teaching them. We present data and findings from our three-year collaboration on this project (2016-2019), which made use of ideas from design research and lesson study, and we discuss lessons learned through our collaboration.

• Speaker: Leonardo Abbrescia, MSU
• Title: Stability of traveling planewave solutions to Lorentzian vanishing mean curvature flow
• Date: 11/21/2019
• Time: 1:00 PM - 1:50 PM
• Place: C517 Wells Hall

Lorentzian minimal submanifolds of Minkowski space are the dynamic analogue of minimal surfaces in the elliptic regime. They are defined by the vanishing of mean curvature, which can be expressed as a system of geometric PDEs. With the requirement that the submanifold be Lorentzian, that is, that the induced metric is Lorentzian, the equations have a hyperbolic nature. Consequently, the natural approach to study them is via the Cauchy initial value problem. In this talk we discuss stability properties of traveling planewave solutions to these equations, and highlight the difficulties introduced by the "infinite energy" planewave background. This is joint work with Willie Wong.

• Speaker: Craig Gross, Rachel Domagalski, MSU
• Title: Git/Github and Zotero Workshop
• Date: 11/21/2019
• Time: 4:00 PM - 5:00 PM
• Place: C204 Wells Hall

The AMS Grad Student Chapter is putting on a Git, GitHub, and Zotero workshop. If you want to know more about version control / staying organized / making .bib files / best collaboration practices, this workshop is for you! Please bring your laptop. Snacks will be provided!

• Speaker: Yeonhyang Kim, Central Michigan University
• Title: Q-ball imaging using predicted diffusion gradient directions
• Date: 11/22/2019
• Time: 4:10 PM - 5:00 PM
• Place: A203 Wells Hall

We review the theory of q-ball imaging and describe a simple linear matrix formulation for the q-ball reconstruction based on spherical harmonic basis function interpolation. In this talk, we present a novel method to improve the q-ball reconstruction by determining appropriate positions at which a synthesized signal is obtained by combining surrounding signals in given diffusion gradient directions.

• Speaker: Boris, Kalinin, Penn State University
• Title: Local rigidity for partially hyperbolic toral automorphisms
• Date: 11/26/2019
• Time: 3:50 PM - 4:50 PM
• Place: C304 Wells Hall

We study perturbations of an irreducible ergodic toral automorphism $L$ with non-trivial center. For a small perturbation $f$ of $L$ with smooth center foliation we obtain results on regularity of the leaf conjugacy to $L$ and of a Holder topological conjugacy to $L$, when it exists. As a corollary, we show that for any symplectic perturbation a Holder conjugacy to $L$ must be smooth. For a totally irreducible $L$ with two-dimensional center, we establish various equivalent conditions that ensure smooth conjugacy between $L$ and $f$. This is joint work with Andrey Gogolev and Victoria Sadovskaya

• Speaker: Sanjay Kumar, MSU
• Title: TBD
• Date: 12/02/2019
• Time: 3:00 PM - 3:50 PM
• Place: C304 Wells Hall

TBD

• Speaker: Neel Patel, University of Michigan
• Title: TBA
• Date: 12/06/2019
• Time: 4:10 PM - 5:00 PM
• Place: A203 Wells Hall

No abstract available.