Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 18, 2021.

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Thursday, February 18, 2021

2:00 pm in Zoom,Thursday, February 18, 2021

Interlacing methods in extremal combinatorics

Hao Huang (Emory University)

Abstract: Extremal Combinatorics studies how large or how small a collection of finite objects could be, if it must satisfy certain restrictions. In this talk, we will discuss how eigenvalue interlacing lead to various interesting results in Extremal Combinatorics, including the Erdos-Ko-Rado Theorem and its degree version, an isodiametric inequality for discrete cubes, and the resolution of a thirty-year-old open problem in Theoretical Computer Science, the Sensitivity Conjecture. A number of open problems will be discussed during this talk.

For Zoom info, please contact jobal@illinois.edu

3:00 pm in Zoom,Thursday, February 18, 2021

Determinantal ideals, pipe dreams, and non-intersecting lattice paths

Li Li   [email] (Oakland University)

Abstract: Determinantal ideals are ideals generated by minors of a variable matrix. They play an important role in both commutative algebra and algebraic geometry. A combinatorial approach to study a determinantal ideal is to apply Groebner degeneration to get a squarefree monomial ideal, and study the corresponding simplicial complex instead. Through this approach, some invariants such as Hilbert polynomials of the ideals can be expressed in terms of pipe dreams and non-intersecting lattice paths. In this talk, I will report recent work on double determinantal ideals, and in particular the combinatorial objects that play the role of non-intersecting lattice paths. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.