• 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: Shelly Harvey, Rice
• Title: TBA
• Date: 09/19/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

TBA

• Speaker: Jeanne Wald, MSU
• Title: Special event: Introductions to Ongoing Undergraduate MTH and STT Research Projects
• Date: 09/20/2019
• Time: 4:10 PM - 5:30 PM
• Place: C304 Wells Hall

Exchange and MSU Student Research Teams will give brief introductions to their research projects.

• Speaker: Corey Jones, The Ohio State University
• Title: The higher dimensional algebra of matrix product operators and quantum spin chains
• Date: 09/26/2019
• Time: 11:30 AM - 12:30 PM
• Place: C304 Wells Hall

In the context of 1D quantum spin chains, matrix product operators provide a way to study non-local operators such as translation in terms of quasi-local information. They have been used to describe a generalized form of symmetry for 1D systems on the boundary of 2D topological phases. In this talk, we will introduce some concepts of higher dimensional algebra, and a broad hypotheses about higher categories and spatially extended quantum systems. We will then explain how the collection of matrix product operators assembles into a higher (symmetric monoidal 2-) category, and discuss some implications of this. Based on joint work with David Penneys.

• Speaker: Joshua Ruiter, Michigan State
• Title: Root systems - a powerful tool for classification
• Date: 09/30/2019
• Time: 4:30 PM - 5:30 PM
• Place: C304 Wells Hall

Root systems arose historically as a tool for classifying semisimple Lie algebras, but they can also be understood without that context. I will describe several concrete examples of root systems, with plenty of pictures. I will describe how to associate a special graph called a Dynkin diagram to a root system, and briefly describe the classification of root systems. If time allows, I will describe some of the applications to classifying semisimple Lie algebras and reductive algebraic groups. All you need to know to understand my talk is how to compute dot products on $\mathbb{R}^n$.

• Speaker: Romyar Sharifi, UCLA
• Title: TBD
• Date: 10/10/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Jesse Madnick , McMaster University
• Title: TBD
• Date: 10/17/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Steven Wise, University of Tennessee, Knoxville
• Title: TBD
• Date: 10/18/2019
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Lev Tovstopyat-Nelip, MSU
• Title: TBA
• Date: 10/24/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Boyu Zhang, Princeton University
• Title: TBD
• Date: 10/31/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Charles Smart, U Chicago
• Title: TBA
• Date: 11/07/2019
• Time: 11:30 AM - 12:30 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Marius Lemm, Harvard
• Title: TBA
• Date: 11/15/2019
• Time: 10:30 AM - 11:30 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Akram Alishahi, University of Georgia
• Title: TBA
• Date: 11/21/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

TBA