Auburn Algebra Seminar
Fall 2025
Schedules from past semestersSeminars will be held in Parker 354 on Tuesdays from 2:30 to 3:20, unless otherwise noted.
Schedule:
August 25 (Monday): Hoa Dinh (Troy University). Note the unusual day!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.)
August 26: Ming-Cheng Tsai (National Sun Yat-sen University)
Title: Multiplicative spectrum and trace preservers on complex and stochastic matrices
Abstract: In this talk, we mainly explore multiplicative spectrum and trace preservers on the set of complex and stochastic matrices. We will give concrete description of spectrum and trace preservers on the sets of complex matrices, doubly stochastic, row stochastic, and column stochastic, respectively. Some related examples and results are provided.
September 2:
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September 9:
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September 16:
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September 23:
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September 30: 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.
October 7: 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.
October 14: Michael Brown (local)
Title: Computing Ext for complexes of sheaves on projective varieties
Abstract: I will describe an effective algorithm for computing Ext between bounded complexes of coherent sheaves on a projective variety. This is joint work with Souvik Dey, Guanyu Li, and Mahrud Sayrafi.
October 21: Hal Schenck (local)
Title: The Likelihood Correspondence
Abstract: An arrangement of hypersurfaces in projective space is strict normal crossing (SNC) if and only if its Euler discriminant is nonzero. We study the critical loci of arbitrary Laurent monomials in the equations of the smooth hypersurfaces. The family of these loci forms an irreducible variety in the product of two projective spaces, known in algebraic statistics as the likelihood correspondence and in particle physics as the scattering correspondence. We establish an explicit determinantal representation for the minimal generators of the bihomogeneous prime ideal that defines this variety.
October 28: John Cobb (local)
Title: Solid State Physics and Algebraic Geometry
Abstract: I’ll describe how a version of spectral graph theory serves as a “tight-binding” model describing electron dynamics in crystalline solids, such as those found in nano-materials and topological insulators. This model turns out to be entirely algebraic and allows one to prove facts about the approximate electronic properties of materials using algebraic geometry and, more generally, interact with a larger world of spectral theory and periodic operators. I’ll spend some time developing this dictionary with lots of pictures, and then I’ll describe upcoming joint work with Matthew Faust and Andreas Kretschmer using some ideas from deformation theory to completely determine when a periodic discrete potential can be isospectral to the trivial potential.
November 4: Justin Lyle (local)
Title: Vanishing of Tor and Depth of Tensor Products
Abstract: Let R be a commutative Noetherian local ring and let M,N be finitely generated R-modules. A classical problem is to calculate the depth of the tensor product of M and N. This turns out to be extremely difficult to do, even under very stringent hypotheses. In this talk, we will discuss some classical work of Auslander, Huneke-Wiegand, Iyengar, and others on this problem, before moving on to discuss recent works of the speaker giving characterizations for rings over which depth of tensor products always behaves ``nicely". This talk is based primarily on joint work with Kaito Kimura and Andrew Soto Levins.
November 11: Michael Perlman (University of Alabama)
Title: Higher singularities for determinantal ideals
Abstract: Higher Du Bois and higher rational singularities are newly-defined properties of complete intersections that can be detected using local cohomology, refining the classical notions of Du Bois and rational singularities. We will discuss the commutative algebra behind these properties, and a number of challenges that arise while attempting to generalize them outside the complete intersection case. Via the example of determinantal ideals, we will describe multiple possible generalizations.
November 18: Luke Oeding (local)
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December 2: Saeed Nasseh (Georgia Southern University)
Title: Connections and lifting theory of DG modules
Abstract: Lifting theory was studied by Auslander, Ding, and Solberg for modules and by Yoshino for complexes. Further progress on this theory has been made recently (in the works of Nasseh, Ono, Sather-Wagstaff, and Yoshino) in the context of differential graded (DG) homological algebra in order to obtain a clearer insight on some major problems in commutative algebra. On the other hand, the notion of connections originates from Riemannian geometry and its history goes back to the nineteenth century in the work of Christoffel. It has been studied since then by several mathematicians and physicists including Alain Connes who generalized it to the context of noncommutative differential geometry. In this talk, I will survey recent developments on the lifting theory of DG modules and describe a relationship between this theory and a DG version of the notion of connections. This is an in-progress joint work with Maiko Ono and Yuji Yoshino.