Algebra Seminars

COSAM Departments Mathematics & Statistics Research Seminars Algebra



Seminars are held in 358 Parker Hall on Tuesdays at 2:30pm.

Upcoming Algebra Seminars

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Past Algebra Seminars
DMS Algebra Seminar
Apr 29, 2025 02:30 PM
ZOOM


datta

Speaker: Rankeya Datta (University of Missouri)

Title: Enhancements of flatness in commutative algebra

Abstract: The notion of flatness plays a fundamental role in algebraic geometry and commutative algebra. A basic property of a flat module is that expansion of ideals to the module commutes with intersection for a finite family of ideals. In this talk I will introduce several enhancements of flat modules that arise from examining the natural question of when ideal expansion to a flat module commutes with intersection for an arbitrary (i.e., possibly infinite) family of ideals. These enhancements of flatness were first explored by Raynaud-Gruson in their work on the faithfully flat descent of projectivity and by Ohm-Rush in their work on content functions and trace ideals. Later, Hochster-Huneke encountered these enhancements in their development of tight closure theory in prime characteristic. Most of my talk will focus on defining and exploring these flatness enhancements and how they relate to each other. A particularly pleasing picture emerges in the local setting. If time permits, I will mention consequences for some outstanding questions in prime characteristic singularity theory.

 
DMS Algebra Seminar
Apr 22, 2025 02:30 PM
354 Parker Hall


Speaker: Jayan Mukherjee (Oklahoma State University)

Title: Syzygies of ribbons on higher genus curves


Abstract: In this talk, we will discuss the syzygies of the canonical embedding of a ribbon \(\widetilde{C}\) on a curve \(C\) of genus \(g \geq 1\). We show that the linear series Clifford index and the resolution Clifford index are equal for a general ribbon of arithmetic genus \(p_a\) on a general curve of genus \(g\) with \(p_{a} \geq \operatorname{max}\{3g+7, 6g-4\}\). Among non-general ribbons, the case of split ribbons is particularly interesting. Equality of the two Clifford indices for a split ribbon is related to the gonality conjecture for \(C\) and it implies Green's conjecture for all double covers \(C'\) of \(C\) with \(g(C') \geq \textrm{max}\{3g+2, 6g-4\}\). We reduce it to the vanishing of certain Koszul cohomology groups of an auxiliary module of syzygies associated to \(C\) , which may be of independent interest.

DMS Algebra Seminar
Apr 08, 2025 02:30 PM
ZOOM


josefranco

Speaker: Jose Franco (University of North Florida)

Title: On the Chaotic Thompson Metric of Matrices

 
Abstract: In this talk, we introduce and study properties of the Thompson metric induced by the chaotic order on the cone of positive definite matrices. Furthermore, we introduce an approach to characterize geodesic curves associated to Thompson metrics and study in-betweenness type results for the metric induced by the chaotic order. Among other results, we obtain that the map \(A\mapsto d_\ll(A,Q_{\alpha,z}(B,A)); \quad z>0,\) satisfies Audenaert's in-betweenness for \(0\le \alpha \le 1\).
DMS Algebra Seminar
Mar 25, 2025 02:30 PM
354 Parker Hall


Speaker: Ian Tan (Auburn University)

Title: Orbits and Invariants in Quantum Information Theory

Abstract: In the field of quantum information theory, one studies—among other things—the information processing tasks that can be achieved by taking advantage of a quantum phenomenon known as entanglement. There is a mathematical formalism that captures the notion of entanglement by elements of a vector space called state vectors. The local unitary and SLOCC (stochastic local operations with classical communication) groups act on this space, producing natural equivalence classes of state vectors. In this work, we consider these group actions and their invariants which are used to classify and distinguish state vectors.

DMS Algebra Seminar
Mar 18, 2025 02:30 PM
354 Parker Hall


pandey

Speaker: Vaibhav Pandey (Purdue University)

Title: Symbolic powers of maximal minors under general linkage



Abstract: The symbolic powers of the minors of a generic matrix are well understood as determinantal rings are Algebras with Straightening Laws (ASLs). In particular, the ASL structure readily yields the fact that the symbolic powers of maximal minors agree with the ordinary powers. We prove that, quite surprisingly, the equality of the symbolic and ordinary powers holds for `the most general link' of maximal minors as well. Better still, the blowup algebras of the general link have precisely the same homological properties as those of the maximal minors. The key point is that these facts do not follow from standard techniques in liaison theory; we develop the novel tool of Gröbner degeneration of links in order to attack the problem. This is joint work with Matteo Varbaro.

DMS Algebra Seminar
Mar 17, 2025 02:30 PM
354 Parker Hall


March 17 (Monday) 

kim

Speaker: Sejong Kim (Chungbuk National University)

Title: Quasi-Wasserstein mean of positive definite matrices



Abstract: The typical examples of Kubo-Ando's operator means are the weighted arithmetic, geometric, and harmonic means, which are monotonically interpolated by the power mean (introduced by Lim and Palfia). There are other important means of non Kubo-Ando's operator means such as the weighted spectral geometric and Wasserstein mean. We define quasi-Wasserstein means, which interpolate the weighted spectral geometric and Wasserstein mean. We study their properties including monotonicity for near-order, trace and norm inequalities.

DMS Algebra Seminar
Mar 04, 2025 02:30 PM
354 Parker Hall


Note the new room this semester!

 

hal

Speaker: Hal Schenck

Title: From approximation theory to homological algebra--splines

 

Abstract: I will discuss the use of homological algebra in attacking a problem in approximation theory: determining the space of piecewise polynomial functions on a polyhedral subdivision of a region in Euclidean space. I will also touch on an interesting connection to toric geometry.

DMS Graduate Student Seminar
Feb 26, 2025 03:00 PM
010 ACLC


brown

Speaker: Dr. Michael Brown (Auburn University)

Title: Introduction to Free Resolutions

 

Abstract: Given a ring R and an R-module M, a free resolution of M is an approximation of M in terms of the simplest kind of module: namely, free modules. Free resolutions play an important role in commutative algebra, algebraic geometry, and many other neighboring fields. This talk will be an introduction to free resolutions: how to construct them, some key results about them, and some open questions.

DMS Algebra Seminar
Dec 03, 2024 02:30 PM
ZOOM


josefranco
 
Speaker: Jose Franco (University of North Florida)
 
Title: A theory of alternative means of matrices
 
 
Abstract: In this talk, we introduce a theory of alternative means of positive definite matrices. We define the alternative mean associated to a normalized operator monotone function by
\(A\hat{\sigma}_f B = f(A^{-1}\sharp B)Af(A^{-1}\sharp B),\)
for positive definite matrices \(A\) and \(B\). We study the adjoint, transpose, and duals of these means and obtain a characterization of the spectral geometric means in terms of alternative means and their duals. Additionally, we show the deep connection between the alternative means and the near order of matrices. In particular, we obtain in-betweenness results of the type \(A\preceq A\hat{\sigma}_f B \preceq B.\)
DMS Algebra Seminar
Nov 19, 2024 02:30 PM
358 Parker Hall


cobb
 
Speaker: John Cobb (Auburn) 
 
For graduate students: John will also give a “pre-talk” aimed at grads starting at 1:50, in the same room, to help supply background for his talk.  
 
Title: Multigraded Syzygies

 
Abstract: I’ll describe two results that fit a recent theme of research in commutative algebra and algebraic geometry: pushing known results from the graded to the multigraded setting. One involves using logic to get a bound on projective dimension (Stillman’s Conjecture), and the other using homological techniques to get a bound on the regularity of curves. In the pretalk, I’ll introduce the main objects and theirs motivation more thoroughly.

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