• Speaker: Nathan Chen, Columbia University
• Title: On the irrationality of some algebraic varieties and their subvarieties
• Date: 10/24/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Laure Flapan (flapanla@msu.edu)

The classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can take on a complementary perspective - given a smooth projective variety whose nonrationality is known, how far is it from being rational? I will survey what is currently known, with an emphasis on hypersurfaces and complete intersections.

• Speaker: Nadia Lafrenière, Dartmouth
• Title: A Study Of Homomesy On Permutations Using The FindStat Database
• Date: 10/26/2022
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

We performed a systematic study of permutation statistics and bijective maps on permutations, looking for the homomesy phenomenon. Homomesy occurs when the average value of a statistic is the same on each orbit of a given map. The maps that exhibit homomesy include the Lehmer code rotation, the reverse, the complement, and the Kreweras complement, all of which have some geometric interpretations. The statistics studied relate to familiar notions such as inversions, descents, and permutation patterns, among others. Beside the many new homomesy results, I’ll discuss our research method, in which we used SageMath to search the FindStat combinatorial statistics database to identify potential instances of homomesy, and what this experiment taught us about the maps themselves and the homomesy phenomenon at large. This is joint work with Jennifer Elder, Erin McNicholas, Jessica Striker and Amanda Welch.

• Speaker: Dapeng Zhan, MSU
• Title: Boundary Green's function and Minkowski content for SLE$_\kappa(\rho)$
• Date: 10/26/2022
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall
• Contact: Dapeng Zhan (zhan@msu.edu)

We prove the existence of the Minkowski content of the intersection of an SLE$_\kappa(\rho)$ curve with a real interval using the standard approach, which is to estimate the convergence rate of one-point and two-point boundary Green's functions of SLE$_\kappa(\rho)$. Then we show the existence of a conformally covariant measure called Minkowski content measure on the intersection of an SLE$_\kappa(\rho)$ curve with a half real line, which is closely related to the Minkowski content. Using the Minkowski content measure, we construct rooted and unrooted SLE$_\kappa(\rho)$ bubble measures, which are supported on loops and satisfy SLE$_\kappa(\rho)$-type domain Markov property.

• Speaker: Guanghui Lan, Georgia Institute of Technology
• Title: 1W-MINDS talk (passcode is the first prime number > 100).
• Date: 10/27/2022
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting)
• Contact: Mark A Iwen ()

See https://sites.google.com/view/minds-seminar/home

• Speaker: Pavel coupek, MSU
• Title: Eigenalgebra over field and over DVR
• Date: 10/27/2022
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

Continuation of previous talk. Following the eigenalgebra book, after considering eigenalgebra over field, if time allow, we will talks about eigenalgebra over dvr

• Speaker: Victor Reiner, University of Minnesota
• Title: Hop on the left-regular band-wagon!
• Date: 10/27/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Joseph Waldron (waldro51@msu.edu)

We will give a gentle introduction to a class of finite semigroups bearing the cryptic name "left-regular bands" (LRBs). These LRBs show up, for example, in the combinatorics of reflection groups and hyperplane arrangements, in the analysis of mixing times for certain card-shuffling Markov chains, as well as in the space of phylogenetic trees. We focus on examples with large groups of symmetries that act on the semigroup algebra of the LRB. Here the well-understood LRB representation theory, together with some combinatorics, allow one to answer two invariant-theory questions: What is the structure of the invariant subalgebra, and how does it act on the whole semigroup algebra? This is based on joint work with Sarah Brauner and Patty Commins (arXiv:2206.11406).