### TBD by Benjamin Lovitz

- Series
- Algebra Seminar
- Time
- Monday, April 22, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Benjamin Lovitz – Northeastern University

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- Series
- Algebra Seminar
- Time
- Monday, April 22, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Benjamin Lovitz – Northeastern University

- Series
- Algebra Seminar
- Time
- Monday, April 8, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Ada Wang – Harvard University

- Series
- Algebra Seminar
- Time
- Monday, April 1, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Andrés R. Vindas Meléndez – University of California, Berkeley

- Series
- Algebra Seminar
- Time
- Monday, March 25, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Frank Sottile – Texas A&M University

- Series
- Algebra Seminar
- Time
- Monday, March 4, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Martin Helmer – North Carolina State University

- Series
- Algebra Seminar
- Time
- Monday, February 26, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Mahrud Sayrafi – University of Minnesota

- Series
- Algebra Seminar
- Time
- Monday, February 19, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Anastasia Nathanson – University of Minnesota

**Please Note:** There will be a pre-seminar (aimed toward grad students and postdocs) from 11:00 am to 11:30 am in Skiles 005.

Given a matroid and a group of its matroid automorphisms, we study the induced group action on the Chow ring of the matroid. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincar\'e duality andthe Hard Lefschetz theorem. We lift these to statements about this permutation action, and suggest further conjectures in this vein.

- Series
- Algebra Seminar
- Time
- Monday, February 12, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Jurij Volčič – Drexel University

**Please Note:** There will be a pre-seminar (aimed toward grad students and postdocs) from 11:00 am to 11:30am in Skiles 005.

Hilbert's Nullstellensatz about zero sets of polynomials is one of the most fundamental correspondences between algebra and geometry. More recently, there has been an emerging interest in polynomial equations and inequalities in several matrix variables, prompted by developments in control systems, quantum information theory, operator algebras and optimization. The arising problems call for a suitable version of (real) algebraic geometry in noncommuting variables; with this in mind, the talk considers matricial sets where noncommutative polynomials attain singular values, and their algebraic counterparts.

Given a polynomial f in noncommuting variables, its free (singularity) locus is the set of all matrix tuples X such that f(X) is singular. The talk focuses on the interplay between geometry of free loci (irreducible components, inclusions, eigenlevel sets, smooth points) and factorization in the free algebra. In particular, a Nullstellensatz for free loci is given, as well as a noncommutative variant of Bertini's irreducibility theorem and its consequences.

- Series
- Algebra Seminar
- Time
- Monday, February 5, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- May Cai and Matt Baker – Georgia Tech

This special algebra seminar will feature short talks by our very own May Cai and Matt Baker, who will speak on the following topics:

May Cai: The completion problem asks one to take a partial observation of some underlying object, and try to recover the original observation. Concretely, we have some object of interest, and a point in the image of that object under a projection map, and want to understand the fiber of this point under this map. In particular, for log-linear models, which are the restrictions of toric varieties to the probability simplex, under certain mild conditions, when this fiber is finite it turns out to have exactly either one or two entries. This is joint work with Cecilie Olesen Recke and Thomas Yahl.

Matt Baker: The determinant of a skew-symmetric matrix has a canonical square root given by the Pfaffian. Similarly, the resultant of two reciprocal polynomials of even degree has a canonical square root given by their reciprocant. Computing the reciprocant of two cyclotomic polynomials yields a short and elegant proof of the Law of Quadratic Reciprocity.

- Series
- Algebra Seminar
- Time
- Monday, January 29, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Papri Dey – Georgia Tech

**Please Note:** There is no pre-seminar this time.

The classical theorems of Perron and Frobenius, which explore spectral properties of nonnegative matrices, have been extensively examined and generalized from various perspectives, including a cone-theoretic (geometric) viewpoint. Concurrently, in the past decade, there has been a notable effort to fuse the techniques of algebraic geometry and combinatorics in an exploration of Lorentzian polynomials by Brändén and Huh, also known as completely log-concave polynomials (CLC) by Anari et.al. or strongly log-concave polynomials by Gurvits.

In this talk, I will discuss my ongoing joint work with Greg Blekherman regarding the class of polynomials with Lorentzian signature (PLS) defined over closed convex cones. This class encompasses various special polynomials, including Lorentzian polynomials over the nonnegative orthant and hyperbolic polynomials over hyperbolicity cones. We establish a compelling connection between PLS over a self-dual cone K and the generalized Perron Frobenius theorem over K. This connection enables us to provide an alternative necessary and sufficient condition to characterize the Lorentzian polynomials.