### TBA

- Series
- Algebra Seminar
- Time
- Tuesday, December 7, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Robert Walker – robmarsw785@gmail.com

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- Series
- Algebra Seminar
- Time
- Tuesday, December 7, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Robert Walker – robmarsw785@gmail.com

- Series
- Algebra Seminar
- Time
- Tuesday, November 30, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Brooke Ullery – Emory University – bullery@emory.edu

- Series
- Algebra Seminar
- Time
- Tuesday, October 26, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Florian Enescu – Georgia State – fenescu@gsu.edu

- Series
- Algebra Seminar
- Time
- Tuesday, October 19, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Matt Baker – Georgia Tech – mbaker@math.gatech.edu

- Series
- Algebra Seminar
- Time
- Tuesday, October 5, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Kaelin Cook-Powell – Emory University – kco279@g.uky.edu

- Series
- Algebra Seminar
- Time
- Tuesday, September 28, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Anton Leykin – Georgia Tech – leykin@math.gatech.edu

- Series
- Algebra Seminar
- Time
- Tuesday, September 21, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Ashley K. Wheeler – Georgia Tech – wheeler@math.gatech.edu

Each point x in Gr(r,n) corresponds to an r×n matrix A_x which gives rise to a matroid M_x on its columns. Gel'fand, Goresky, MacPherson, and Serganova showed that the sets {y∈Gr(r,n)|M_y=M_x} form a stratification of Gr(r,n) with many beautiful properties. However, results of Mnëv and Sturmfels show that these strata can be quite complicated, and in particular may have arbitrary singularities. We study the ideals I_x of matroid varieties, the Zariski closures of these strata. We construct several classes of examples based on theorems from projective geometry and describe how the Grassmann-Cayley algebra may be used to derive non-trivial elements of I_x geometrically when the combinatorics of the matroid is sufficiently rich.

- Series
- Algebra Seminar
- Time
- Tuesday, September 14, 2021 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Justin Chen – ICERM/Georgia Tech – justin_chen2@brown.edu

Primary decomposition is an indispensable tool in commutative algebra, both theoretically and computationally in practice. While primary decomposition of ideals is ubiquitous, the case for general modules is less well-known. I will give a comprehensive exposition of primary decomposition for modules, starting with a gentle review of practical symbolic algorithms, leading up to recent developments including differential primary decomposition and numerical primary decomposition. Based on joint works with Yairon Cid-Ruiz, Marc Harkonen, Robert Krone, and Anton Leykin.

- Series
- Algebra Seminar
- Time
- Wednesday, March 24, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Netanel Friedenberg – Georgia Tech – nfriedenberg3@gatech.edu

After reviewing classical results about existence of completions of varieties, I will talk about a class of degenerations of toric varieties which have a combinatorial classification - normal toric varieties over rank one valuation rings. I will then discuss recent results about the existence of equivariant completions of such degenerations. In particular, I will show a result from my thesis about the existence of normal equivariant completions of these degenerations.

BlueJeans link: https://bluejeans.com/909590858?src=join_info

- Series
- Algebra Seminar
- Time
- Wednesday, March 17, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Lars Kühne – University of Copenhagen – lk@math.ku.dk

**Please Note:** This talk will be given via BlueJeans: https://bluejeans.com/531363037

In the talk, I will present an equidistribution result for families of (non-degenerate) subvarieties in a (general) family of abelian varieties. This extends a result of DeMarco and Mavraki for curves in fibered products of elliptic surfaces. Using this result, one can deduce a uniform version of the classical Bogomolov conjecture for curves embedded in their Jacobians, namely that the number of torsion points lying on them is uniformly bounded in the genus of the curve. This has been previously only known in few cases by work of David--Philippon and DeMarco--Krieger--Ye. Finally, one can obtain a rather uniform version of the Mordell-Lang conjecture as well by complementing a result of Dimitrov--Gao--Habegger: The number of rational points on a smooth algebraic curve defined over a number field can be bounded solely in terms of its genus and the Mordell-Weil rank of its Jacobian. Again, this was previously known only under additional assumptions (Stoll, Katz--Rabinoff--Zureick-Brown).

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