### Symplectic/Poisson organizational meeting

Date | Jan 31, 2022 |

Time | 3:00 pm |

Location | 347 Altgeld Hall |

Speaker | Organizational Meeting |

Contact | Joey Palmer |

jpalmer5@illinois.edu | |

Sponsor | Symplectic and Poisson geometry seminar |

### Graph Theory and Combinatorics Seminar: Ryser's Theorem for rho-Latin Rectangles

Date | Feb 1, 2022 |

Time | 1:00 pm |

Location | Zoom |

Speaker | Amin Bahmanian (Illinois State University) |

Contact | Sean English |

Sponsor | N/A |

Let L be an n x n array whose top left r x s subarray is filled with k different symbols, each occurring at most once in each row and at most once in each column. We find necessary and sufficient conditions that ensure the remaining cells of L can be filled such that each symbol occurs at most once in each row and at most once in each column, and each symbol occurs a prescribed number of times in L. The case where the prescribed number of times each symbol occurs is n was solved by Ryser (1951), and the case s=n was settled by Goldwasser et al. (2015). Our technique leads to a very short proof of the latter.

Date | Feb 3, 2022 |

Time | 1:00 pm |

Location | https://illinois.zoom.us/j/83444025985?pwd=MEZxTEtPTlhmTE5WN0k2UVRaWHFkUT09 |

Speaker | Eric Sharpe, Virginia Tech |

Contact | Sheldon Katz |

katzs@illinois.edu | |

Sponsor | n/a |

Abstract: In this talk I will review work on `decomposition,' a property of 2d quantum field theories with 1-form symmetries and, more generally, d-dim'l theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are equivalent to ('decompose into’) disjoint unions of other QFTs, known in this context as "universes.”

Examples include two-dimensional gauge theories and orbifolds with matter invariant under a subgroup of the gauge group. Decomposition explains and relates several physical properties of these theories -- for example, restrictions on allowed instantons arise as a "multiverse interference effect" between contributions from constituent universes. First worked out in 2006 as part of efforts to understand string propagation on stacks, decomposition has been the driver of a number of developments since. In the first half of this talk, I will review decomposition; in the second half, I will focus on the recent application to anomaly resolution of Wang-Wen-Witten in two-dimensional orbifolds.

### Math Department Disability Workshop

Date | Feb 3, 2022 |

Time | 4:00 pm - 5:00 pm |

Location | https://illinois.zoom.us/j/86298267142?pwd=L3dWRU9SUTlmcWtTa21lSm5pM1hPUT09 |

Contact | Grace McCourt |

mccourt4@illinois.edu | |

Sponsor | GEO Disability Caucus |

GEO Disability Caucus is running a workshop aimed at math department TAs, faculty, and instructors to answer these questions and more. The workshop will take place over Zoom, on Thursday Feb. 3 at 4pm. We will cover best practices for engaging with disabled students and the accommodations process, as well as language and definitions, and the context of disability within the university and society. There will also be plenty of examples, and you are welcome to bring any questions you have!

### Number Theory Seminar: The Sixth Moment of Automorphic L-Functions

Date | Feb 8, 2022 |

Time | 11:00 am |

Location | Contact ford@math.uiuc.edu for Zoom link |

Speaker | Josh Stucky |

Contact | Kevin Ford |

ford@math.uiuc.edu | |

Sponsor | n/a |

Abstract: Moments of L-functions are among the central objects of study in modern analytic number theory. In this talk I will discuss my recent results concerning the sixth moment of a family of GL(2) automorphic L-functions. Before discussing my results, I will introduce moments and families of L-functions in some generality, as well as provide some background on the specific family of L-functions I study in my paper. In particular, I will discuss previous results as well as some of the tools used to study this family. As such, the talk should be interesting and accessible to a wide audience including both experts and graduate students.

### Graph Theory and Combinatorics Seminar: Dirac's Theorem for Hamiltonian Berge cycles in uniform hypergraphs

Date | Feb 8, 2022 |

Time | 1:00 pm |

Location | 345 AH |

Speaker | Grace McCourt (UIUC) |

Contact | Sean English |

senglish@illinois.edu | |

Sponsor | N/A |

The famous Dirac's Theorem gives an exact bound on the minimum degree of an n-vertex graph guaranteeing the existence of a Hamiltonian cycle. Last semester at this seminar, Ruth Luo presented exact bounds of similar type for Hamiltonian Berge cycles in r-uniform, n-vertex hypergraphs for all 2 < r < n. This talk will present bounds on the minimum degree guaranteeing existence of Berge cycles of length at least k in such hypergraphs. The bounds are exact for all k at least n/2, and the bounds differ for r less than n/2 and r at least n/2.

This is joint work with Alexandr Kostochka and Ruth Luo.

### Diversity, Inclusion, Equity, and Settler Colonialism in Mathematics

Date | Feb 9, 2022 |

Time | 4:00 pm - 5:00 pm |

Location | Contact na17 AT illinois DOT edu for Zoom details |

Speaker | Belin Tsinnajinnie |

Contact | Nachiketa Adhikari |

na17@illinois.edu | |

Sponsor | AWM |

Abstract: In this talk, I discuss diversity and inclusion initiatives through lens that is informed by frameworks that identify mathematics education as settler colonialism and my own experiences of inclusion/exclusion. I call for a shift in the ways we can frame conversations of justice, equity, diversity, and inclusion in mathematics by asking: How do diversity and inclusion efforts in mathematics and mathematics education directly empower marginalized communities?

*About Belin Tsinnajinnie:*

Belin Tsinnajinnie (he/him) is Diné and Filipinx from Na’ Neelzhiin, New Mexico. Belin received his PhD in Mathematics at the University of Arizona with a doctoral thesis focused on notions of mathematical identity in the context of Indigenous and Latinx students. Belin served as an Assistant Professor of Mathematics for 8 years at the Institute of American Indian Arts followed by 4 years as an Assistant Professor of Mathematics at Santa Fe Community College. Belin is now a Research Associate II at WestEd. Belin is interested in identifying and articulating issues pertaining social justice and equity in mathematics education through Indigenous perspectives.

### Student Cluster Algebra Seminar

Date | Feb 10, 2022 |

Time | 2:00 pm |

Location | Algeld 345 |

Speaker | Trung Vu |

Contact | Trung Vu |

hvu@illinois.edu | |

Sponsor | n/a |

Yang-Baxter equation is an important matrix functional equation introduced in statistical mechanics. Yang-Baxter equation is extermely important in the area of quantum integrability and the framework of quantum inverse scattering method developed by Faddeev in the 80s-90s. In this seminar. In this seminar, I will introduce the Yang-Baxter equation and some of its simple solutions along with the toy model XXX, XXZ and XYZ Heisenberg Chain

### Einstein metrics with prescribed conformal infinity

Date | Feb 11, 2022 |

Time | 1:00 pm |

Location | 147 Altgeld Hall |

Speaker | Xinran Yu |

Contact | Ryan Mitchell |

ryanm12@illinois.edu | |

Sponsor | n/a |

Abstract: Given a conformal class of metrics on the boundary of a manifold, one can ask for the existence of an Einstein metric whose conformal infinity satisfies the boundary condition.

In 1991, Graham and Lee studied this boundary problem on the hyperbolic ball. They proved the existence of metrics sufficiently close to the round metric on a sphere by constructing approximate solutions to a quasilinear elliptic system. In his monograph (2006), Lee discussed the boundary problem on a smooth, compact manifold-with-boundary. Using a similar construction, he proved the existence and regularity results for metrics sufficiently close to a given asymptotically hyperbolic Einstein metric. The proof is based on a linear theory for Laplacian and the inverse function theorem.

### Graduate Student Homotopy Theory Seminar: An Introduction to Exodromy

Date | Feb 11, 2022 |

Time | 3:00 pm |

Location | 341 Altgeld Hall |

Speaker | Brian Shin |

Contact | Doron Grossman-Naples |

doronlg2@illinois.edu | |

Sponsor | n/a |

Abstract: One of the first major topics we learn about in algebraic topology is the classification of locally constant sheaves of sets (i.e. covering spaces) of a sufficiently nice topological space in terms of its fundamental group. This classification is mediated by an equivalence of categories known as the monodromy equivalence. An insight of Kan was that, in order to classify locally constant sheaves of more interesting objects, one must pass from fundamental groups to fundamental infinity-groupoid. In this expository talk, I'd like to talk about work of Barwick-Glasman-Haine pushing this circle ideas further into the realm of stratified spaces. The main result is the exodromy equivalence, which classifies constructible sheaves on a stratified space in terms of its profinite stratified shape.