Kalina Mincheva

Algebra and Combinatorics Seminar

We meet weekly on Wednesday at 3:00 PM (Central time), GI 310

Organizers: Alessandra Constantini and Kalina Mincheva.

Spring 2025

• Souvik Dey, Charles University, Prague.
  Rings with extremal cohomology annihilator. abstract.
  The cohomology annihilator of Noetherian algebras was defined by Iyengar and Takahashi in their work on strong generation in the module category. For a commutative Noetherian local ring, it can be observed that the cohomology annihilator ideal is the entire ring if and only if the ring is regular. Motivated by this, I will consider the question: When is the cohomology annihilator ideal of a local ring equal to the maximal ideal? I will discuss various ring-theoretic and category-theoretic conditions towards understanding this question and describe applications for understanding when the test ideal of the module closure operation on cyclic surface quotient singularities is the maximal ideal.

• Paolo Mantero, University of Arkansas.
  From Interpolation problems to matroids. abstract.
  Interpolation problems are long-standing problems at the intersection of Algebraic Geometry, Commutative Algebra, Linear Algebra and Numerical Analysis, aiming at understanding the set of all polynomial equations passing through a given finite set X of points with given multiplicities. In this talk we discuss the problem for matroidal configurations, i.e. sets of points arising from the strong combinatorial structure of a matroid. Starting from the special case of uniform matroids, we will discover how an interplay of commutative algebra and combinatorics allows us to solve the interpolation problem for any matroidal configuration. It is the widest class of points for which the interpolation problem is solved. Along the way, we will touch on several open problems and conjectures. The talk is based on joint projects with Vinh Nguyen (U. Arkansas).

• Edna Jones, Tulane University.
  Versions of the circle method. abstract.
  The circle method is a useful tool in analytic number theory and combinatorics. The term "circle method" can refer to one of a variety of techniques for using the analytic properties of the generating function of a sequence to obtain an asymptotic formula for the sequence. We will discuss different versions of the circle method and some results that can be obtained by using the circle method.

• Ngo Viet Trung, Institute of Math, Vietnam Academy of Science and Technology.
  Ear decompositions of graphs: an unexpected tool in Combinatorial Commutative Algebra. abstract.
  Ear decomposition is a classical notion in Graph Theory. It has been shown in [1, 2] that this notion can be used to solve difficult problems on homological properties of edge ideals in Combinatorial Commutative Algebra. This talk presents the main combinatorial ideas behind these results.
  [1] H.M. Lam and N.V. Trung, Associated primes of powers of edge ideals and ear decompositions of graphs, Trans. AMS 372 (2019)
  [2] H.M. Lam, N.V. Trung, and T.N. Trung, A general formula for the index of depth stability of edge ideals, Trans. AMS, to appear.

• Alessandra Constantini, Tulane University
  A combinatorial method for the reduction number of an ideal. abstract.
  In the study of commutative rings, several algebraic properties are captured by numerical invariants which are defined in terms of ideals and their powers. Among these, of particular relevance are the reduction number and analytic spread of an ideal, which control the growth of the powers of the given ideal for large exponents. Unfortunately, these invariants are usually difficult to calculate for arbitrary ideals, and different methods might be required depending on the specific features of the class of ideals under examination. In this talk, I will discuss a combinatorial method to calculate the reduction number of an ideal, based on a homological characterization in terms of the regularity of a graded algebra. This is part of ongoing joint work with Louiza Fouli, Kriti Goel, Haydee Lindo, Kuei-Nuan Lin, Whitney Liske, Maral Mostafazadehfard and Gabriel Sosa.

• Sankhaneel Bisui, Arizona State University.
  TBA. abstract.
  TBA.

• Dipendranath Mahato, Tulane University.
  TBA. abstract.
  TBA.

• Thai Nguyen, University of Dayton.
  TBA. abstract.
  TBA.

• Michael Allen, LSU.
  TBA. abstract.
  TBA.

• Yairon Cid-Ruiz, North Carolina State University.
  TBA. abstract.
  TBA.

• Andrés Jaramillo Puentes, University of Tübingen.
  TBA. abstract.
  TBA.

• Andreas Mono, Vanderbilt University.
  TBA. abstract.
  TBA.

• Katia Consani, Johns Hopkins University.
  TBA. abstract.
  TBA.

Past seminars.