Algebra Seminars
Seminars are held in 354 Parker Hall on Tuesdays at 2:30pm.
Oct 07, 2025 02:30 PM
354 Parker Hall
Speaker: Boyana Martinova (University of Wisconsin).
Title: Asymptotic Syzygies of Weighted Projective Spaces
Abstract: What can we say about the syzygies of a module when computing the minimal free resolution explicitly is too computationally intensive? In 2012, Ein and Lazarsfeld gave a description of the nonvanishing syzygies of Veronese embeddings of projective space (even in cases where the minimal free resolution is unknown): for sufficiently large embedding degree, "almost every" allowable Betti entry is nonzero. Later, Ein, Erman, and Lazarsfeld proved the same nonvanishing result using a surprisingly simple method relying entirely on monomials. In this talk, I will discuss some recent work extending these results to the weighted projective setting via an analogue of the EEL Method, and I will highlight some of the challenges that arise when the coordinate ring is nonstandard graded.
DMS Algebra Seminar
Sep 30, 2025 02:30 PM
354 Parker Hall
Speaker: Maria Akter (University of Alabama)
Title: \(m\)-adic Continuity of Frobenius Splitting Ratio
Abstract: The study of singularities under perturbation is classical, with origins dating back to the 50's and 60's through the work of Samuel and Hironaka. In this talk, we introduce the theory of \(F\)-singularities in prime characteristic rings and examine continuity problems in relation to perturbation theory. Our main result characterizes the continuity of the \(F\)-splitting ratio.
DMS Graduate Student Seminar
Sep 17, 2025 03:00 PM
354 Parker Hall
DMS Algebra Seminar
Aug 26, 2025 02:30 PM
354 Parker Hall
DMS Algebra Seminar
Aug 25, 2025 02:30 PM
354 Parker Hall
Title: Quantum algorithms for Kubo-Ando means
Abstract: In this talk, we discuss the construction of a quantum algorithm for computing Kubo–Ando means. We also show how similar techniques can be extended to Bures means, weighted spectral geometric means, power means, and other related matrix means.)
DMS Algebra Seminar
Apr 29, 2025 02:30 PM
ZOOM
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
Speaker: Jose Franco (University of North Florida)
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
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.