Current Seminars
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COMA/NAG Joint Graduate Student Seminar: "Factoriality of LSS ideals"
Location: SLMath: Eisenbud Auditorium, Online/Virtual Speakers: Eliana Tolosa Villarreal (Università di Genova)Lovász-Saks-Schrijver ideals, LSS ideals for short, are a family of ideals associated to graphs that were introduced in the context of orthogonal representations of graphs and studied for the first time in 1989 by Lovász, Saks and Schrijver. The study of such ideals lie in the intersection between algebraic geometry, commutative algebra and combinatorics as some geometric and algebraic properties can be exhibited from combinatorial invariants of the graph and viceversa. Our goal is to study this relationship, focusing on some algebraic properties of LSS ideals such as defining a unique factorization domain.
All are welcome!
Updated on May 13, 2024 08:13 AM PDT -
COMA Colloquium: "Koszul Binomial Edge Ideals"
Location: SLMath: Eisenbud Auditorium, Online/Virtual Speakers: Irena Peeva (Cornell University)Koszul algebras appear in many areas of algebra, geometry and topology. Two of their
remarkable properties are that the minimal free resolution of the ground field k can be explicitly
described as a generalized Koszul complex, and there is an elegant formula relating the Hilbert
function of the algebra and the Poincare series of k. Consider the binomial edge ideal J(G) associated
to a finite simple graph G. Such an ideal is always generated by quadrics. It has a quadratic Groebner
basis if and only if the graph G is closed. There are many other cases when J(G) is Koszul. The study
of Koszul binomial edge ideals was initiated by V. Ene, J. Herzog, and T. Hibi in 2014. We characterize
the Koszul binomial edge ideals by a simple combinatorial property of G. This is joint work with
A. LaClair, M. Mastroeni, and J. McCullough.Updated on May 13, 2024 08:27 AM PDT
Upcoming Seminars
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COMA Special Topic: Mixed characteristic analogues of F-injective and Du Bois singularities"
Location: SLMath: Online/Virtual, Eisenbud Auditorium Speakers: Joseph Waldron (Michigan State University)Singularities are measured in different ways in characteristic zero, positive characteristic, and mixed characteristic. However, the classes of singularities usually form analogous groups with similar properties, with an example of such a group being klt, strongly F-regular and BCM-regular. In this talk we shall focus on a mixed characteristic counterpart of F-injective and Du Bois singularities. We will see that the three have a unified description and satisfy many expected properties.
Updated on May 15, 2024 12:37 PM PDT -
COMA Working Group: Set Theoretic Complete Intersections
Location: SLMath: Baker Board RoomUpdated on Feb 15, 2024 10:39 AM PST -
COMA Colloquium: "Towards an analogue of F-signature functions in mixed characteristic"
Location: SLMath: Eisenbud Auditorium, Online/Virtual Speakers: Kevin Tucker (University of Illinois at Chicago)In positive characteristic, the F-
signature can be viewed as a quantitative measure of F-regularity – an important class of singularities central to the celebrated theory of tight closure pioneered by Hochster and Huneke, and closely related to
Kawamata Log Terminal (KLT) singularities via standard reduction techniques from characteristic zero. The definition can also be extended to divisor (or hypersurface) pairs, and the resulting F-signature functions given by scaling enjoy a number of nice properties such as convexity. In this talk, I will give an overview of some of the positive characteristic theory, and detail recent progress in developing an analogue in the mixed characteristic setting. Based in part on joint work with Hanlin Cai, Seungsu Lee, Linquan Ma, and Karl Schwede, this involves leveraging the perfectoidization functor of Bhatt-Scholze to define the perfectoid signature. In addition, I will mention joint work in progress with a subset of the same authors to extend this definition to pairs and show properties of the resulting perfectoid signature functions given by scaling.Updated on May 16, 2024 08:18 AM PDT -
COMA Working Group: Syzygies: "Minimal Resolutions and the Homology of Matching and Chessboard Complexes, by Victor Reiner and Joel Roberts"
Location: SLMath: Baker Board Room Speakers: Ethan Reed (University of Notre Dame)Updated on May 16, 2024 01:56 PM PDT -
COMA Seminar: "Methods to Extend the Classical Multiplicities to General Ideals"
Location: SLMath: Eisenbud Auditorium, Front Courtyard Speakers: Yu Xie (Widener University)In this talk, I will discuss two methods: the 0th local cohomology and the bigraded algebra, that are used to extend the classical multiplicities such as the Hilbert-Samuel multiplicity, the Hilber-Kunz multiplicity, the mixed multiplicity from 0-dimensional ideals to general ideals.
Updated on May 16, 2024 01:58 PM PDT -
COMA Seminar
Location: SLMath: Eisenbud Auditorium, Online/VirtualUpdated on Mar 14, 2024 02:18 PM PDT
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ADJOINT 2024
ADJOINT is a yearlong program that provides opportunities for U.S. mathematicians – especially those from the African Diaspora – to conduct collaborative research on topics at the forefront of mathematical and statistical research. Participants will spend two weeks taking part in an intensive collaborative summer session at SLMath (formerly MSRI). The two-week summer session for ADJOINT 2024 will take place June 24 to July 5, 2024 in Berkeley, California. Researchers can participate in either of the following ways: (1) joining ADJOINT small groups under the guidance of some of the nation's foremost mathematicians and statisticians to expand their research portfolio into new areas, or (2) applying to Self-ADJOINT as part of an existing or newly-formed independent research group to work on a new or established research project. Throughout the following academic year, the program provides conference and travel support to increase opportunities for collaboration, maximize researcher visibility, and engender a sense of community among participants.
Updated on Apr 10, 2024 10:50 AM PDT
Past Seminars
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Seminar COMA Seminar: "Singularities in Mixed Characteristic via Alterations"
Updated on May 09, 2024 03:14 PM PDT -
Seminar COMA Colloquium: "Singularities of ideals admitting a squarefree Gröbner degeneration"
Updated on May 09, 2024 02:44 PM PDT -
Seminar COMA Working Group: Quasi-F Splitting
Updated on Feb 09, 2024 01:22 PM PST -
Seminar COMA/NAG Joint Graduate Student Seminar
Updated on Feb 20, 2024 12:44 PM PST -
Seminar NAG Colloquium: "Projective stacks"
Updated on May 09, 2024 02:45 PM PDT -
Seminar COMA Working Group: Set Theoretic Complete Intersections
Updated on Feb 15, 2024 10:37 AM PST -
Seminar COMA Special Topic: "Some limitations of reduction mod p methods"
Updated on May 09, 2024 03:13 PM PDT -
Seminar Movie Night: "N is a number: a portrait of Paul Erdős"
Created on Apr 25, 2024 11:14 AM PDT -
Seminar COMA Colloquium: "Vanishing Orders of Functions Along Singularities and Ideal Containment Problems in Noetherian Rings"
Updated on Apr 30, 2024 08:11 AM PDT -
Seminar NAG Equivariant Derived Categories Seminar: "Window kernels"
Updated on May 03, 2024 10:21 AM PDT -
Seminar COMA Seminar: "Explicit constructions of short virtual resolutions"
Updated on May 03, 2024 09:17 AM PDT -
Seminar NAG Categorical Enumerative Invariants Seminar: "CEI, computational aspects and open questions"
Updated on May 08, 2024 09:46 AM PDT -
Seminar COMA Working Group: Syzygies: "Linear syzygies of projective space, by Michael Kemeny"
Updated on May 03, 2024 09:15 AM PDT -
Seminar COMA Colloquium: "Local cohomology of subspace arrangements"
Updated on May 03, 2024 08:48 AM PDT -
Seminar COMA Working Group: Quasi-F Splitting
Updated on Feb 09, 2024 01:22 PM PST -
Seminar Commutative Algebra + Algebraic Geometry Seminar: "Classifying numerical semigroups using polyhedral geometry" & "Two bounds on Castelnuovo-Mumford regularity"
Updated on May 03, 2024 09:31 AM PDT -
Seminar NAG Donaldson-Thomas Theory Seminar: "4-dimensional Donaldson-Thomas theory”
Updated on May 03, 2024 11:38 AM PDT -
Seminar NAG Colloquium: "Local duality, regularity and completions for stable categories of modular representations"
Updated on May 03, 2024 09:10 AM PDT -
Seminar COMA Working Group: Set Theoretic Complete Intersections
Updated on Feb 15, 2024 10:35 AM PST -
Seminar COMA Memoriam in honor of the life and work of Jürgen Herzog
Updated on Apr 24, 2024 11:52 AM PDT -
Seminar COMA Seminar
Updated on Mar 14, 2024 02:16 PM PDT -
Seminar COMA/NAG Joint Graduate Student Seminar: "Rees algebras of ideals of faces versus Lefschetz properties of nonface ideals"
Updated on Apr 26, 2024 10:30 AM PDT -
Seminar NAG Equivariant Derived Categories Seminar
Updated on Feb 15, 2024 10:35 AM PST -
Seminar COMA/NAG Joint Lunch Seminar: "Ernst Kunz' idea for classifying numerical semigroups"
Updated on Apr 03, 2024 07:56 AM PDT -
Seminar COMA Working Group: Quasi-F Splitting
Updated on Feb 09, 2024 01:22 PM PST -
Seminar Commutative Algebra + Algebraic Geometry Seminar: "Splitting of vector bundles on toric varieties" & "Finding special line bundles on special tetragonal curves"
Updated on Apr 26, 2024 09:25 AM PDT -
Seminar COMA Working Group: Set Theoretic Complete Intersections
Updated on Mar 06, 2024 10:33 AM PST -
Seminar COMA Fellowship of the Rings Talk
Updated on Mar 06, 2024 10:48 AM PST -
Seminar NAG Colloquium: "Moduli of A-infinity algebras and NC geometry"
Updated on Apr 25, 2024 10:34 AM PDT -
Seminar COMA Special Topic: "Module schemes in invariant theory"
Updated on Apr 25, 2024 01:42 PM PDT