Seminars and Colloquia by Series

TBA

Series
Algebra Seminar
Time
Tuesday, November 30, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Brooke UlleryEmory University

TBA

Series
Algebra Seminar
Time
Tuesday, October 26, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Florian EnescuGeorgia State

TBA

Series
Algebra Seminar
Time
Tuesday, October 5, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kaelin Cook-PowellEmory University

Geometric equations for matroid varieties

Series
Algebra Seminar
Time
Tuesday, September 21, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ashley K. WheelerGeorgia Tech

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. 

(Differential) primary decomposition of modules

Series
Algebra Seminar
Time
Tuesday, September 14, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin ChenICERM/Georgia Tech

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.

Equivariant completions for degenerations of toric varieties

Series
Algebra Seminar
Time
Wednesday, March 24, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Netanel FriedenbergGeorgia Tech

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

Equidistribution and Uniformity in Families of Curves

Series
Algebra Seminar
Time
Wednesday, March 17, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Lars KühneUniversity of Copenhagen

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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