Upcoming Colloquia for Spring 2024
Science Hall 107
12:00PM refreshments  12:30PM  1:30PM
Zoom: Link
Science Hall 107
12:00PM refreshments  12:30PM  1:30PM
Zoom: Link
January 26 
Speaker: Sumeyra Sakalli, University of Arkansas In this talk, I will describe my research on exotic 4manifolds in relation to complex surfaces, algebraic fibrations, singularities and also knots. In particular, I will present our constructions of the smallest exotic 4manifolds with nonnegative signatures; deformation and splitting singularities in algebraic fibrations; and generalized chain surgeries, which are symplectic operations we defined, and are useful for building exotic 4manifolds. I will also discuss slice knots in definite 4manifolds. Some of these works are joint with Akhmedov, Karakurt, KjuchukovaMillerRay, Park, Van HornMorris and Yeung. 
January 22 
Speaker: Keegan Boyle, University of British Columbia Title: Alexander Polynomials and Symmetric Knots Abstract: The Alexander polynomial is an invariant of a knot in the 3sphere, defined in terms of the homology of a particular covering space of the knot complement. It is easy to compute and contains significant geometric information about the knot. Consequently, it has received a lot of attention in the literature over the last century. In this talk, I will discuss several of my recent theorems about the Alexander polynomial. These theorems indicate how new geometric information about the knot can be extracted from the polynomial in the presence of a symmetry, and have applications to 4manifold topology. The proofs of these theorems include a mix of classical tools and methods from algebraic and geometric topology, and modern inventions such as Heegaard Floer homology. 
January 19 
Speaker: William Balderrama, University of Virginia Title: Equivariant Maps Between Spheres Abstract 
December 1 
Speaker: Søren Galatius, University of Copenhagen, Denmark 
December 1 
Speaker: Naoki Masuda, University at Buffalo (North Campus) 
November 17 
Speaker: Chris Peterson, Colorado State University 
November 10 
Speaker: Chris Peterson, Colorado State University 
November 3 
Speaker: Boyu Li, NMSU 
October 27 O'Donnell Hall 111 1:00PM  2:00PM 
Speaker: Agnès Beaudry, University of Colorado The new tricks and treats presented today are joint with my fellow peanuts: Lewis, May (not Gaunce and Peter, but Chloe and Clover), Sabrina Pauli and Liz Tatum. 
October 27 O'Donnell Hall 111 2:30PM  3:30PM 
Speaker: Katherine Poirier, New York City College of Technology 
October 27 O'Donnell Hall 111 4:00PM  5:00PM 
Speaker: Zhouli Xu, University of California at San Diego 
October 20 
Speaker: Andrew Comech, Texas A&M The main result of the talk is the spectral stability (absence of linear instability) of solitary waves in the nonlinear Dirac equation with the scalar selfinteraction, known as the Soler model. The stability takes place when certain relation between powers of nonlinearity and the spatial dimension is satisfied. We will illustrate some ideas of the proof on simpler models: nonlinear wave equation and nonlinear Schrodinger equation. This is a joint research with Nabile Boussaid, University Franche—Comte (Besancon). The results are available in: Nabile Boussaid, Andrew Comech, Spectral stability of small amplitude solitary waves of the Dirac equation with the Solertype nonlinearity, Journal of Functional Analysis 277 (2019), 108289. 
October 6 
Speaker: Arvind Kumar, NMSU 
September 22 
Speaker: Frank Sottile, Texas A&M University 
September 1 
Speaker: Yang Hu, NMSU 
August 25 
Speaker: Michael DiPasquale, NMSU In the remainder of the talk we will focus on the representation of an affine semigroup as a quotient of a polynomial ring by a socalled toric ideal. A Gr\"obner basis for the toric ideal possesses a wealth of information about the semigroup, and it is of particular interest both in pure and applied algebraic geometry to find a Gr\"obner basis of low degree. Time permitting we will touch on two projects where we find a Gr\"obner basis of quadrics for combinatorially meaningful classes of toric ideals. 
September 22 
Speaker: Frank Sottile, Texas A&M University 
September 1 
Speaker: Yang Hu, NMSU 
August 25 
Speaker: Michael DiPasquale, NMSU In the remainder of the talk we will focus on the representation of an affine semigroup as a quotient of a polynomial ring by a socalled toric ideal. A Gr\"obner basis for the toric ideal possesses a wealth of information about the semigroup, and it is of particular interest both in pure and applied algebraic geometry to find a Gr\"obner basis of low degree. Time permitting we will touch on two projects where we find a Gr\"obner basis of quadrics for combinatorially meaningful classes of toric ideals. 


April 28 
Speaker: Samuel Scarpino, Northeastern University 
April 21 
Speaker: Boris Choy, University of Sydney Business School 
April 14 
Speaker: Stephen Brazil, Actuary, USA 
March 24 
Speaker: Marco Aiello, University of Stuttgart, Germany 
March 3 
Speaker: Eugene Bilokopytov from University of Alberta, Canada 
February 24 
Speaker: Alexander Shen, University of Montpellier 2, France Title: Information Inequalities Abstract: The intuitive notion of "amount of information" can be formalized in may ways. The algorithmic information (Kolmogorov complexity) theory says that the amount of information in a finite object x is the minimal length of a program that produces x. Some intuitive properties of information (say, the amount of information in pair (x,y) is bounded by the sum of the amounts of information in x and y) can be proven. Another way to measure information is suggested by Shannon information theory. It turns out that the "laws of information theory" (understood as linear inequalities) are the same for both cases (Romashchenko), and the same class of inequalities appears in group theory, database theory, geometric dimension theory. A survey of these results will be given. 
January 25 
Speaker: Yairon CidRuiz, KU Leuven, Belgium Title: Rees algebras of determinantal ideals Abstract: We will give an introduction to SAGBI basis theory and its application to the Rees algebra. We then present a couple of recent results using SAGBI basis theory to find the presentation equations of Rees algebras of determinantal ideals and their properties. 
January 23 
Speaker: Boyu Li, University of Waterloo Title: Analysis on Semigroups Through the Lens of Dilation Theory Abstract: The analysis of algebraic structures using bounded linear operators on Hilbert spaces traces back to the pioneering work of Murray and von Neumann. For example, the abstract harmonic analysis of groups relates various properties of a group to its unitary representations. For semigroups, however, the lack of inverse leads to much richer classes of representations. These representations are often interrelated via dilation theorems. In this talk, I will briefly go over the history of the analysis of semigroups, with a focus on the role of dilation theory. I will then explain how our recent dilation theorem on semigroup dynamical systems unifies many earlier results in dilation theory. This is partly based on joint work with Marcelo Laca. 
January 20 
Speaker: Michael DiPasquale, University of South Alabama Title: A Bridge Between the Algebra and Geometry of Hyperplane Arrangements Abstract: A hyperplane arrangement is a union of codimension one linear spaces. These simple objects provide fertile ground for interactions between combinatorics, algebra, algebraic geometry, topology, and group actions. The combinatorics of an arrangement is encoded by the pattern of intersections among the hyperplanes, called its intersection lattice. On the other hand, a key algebraic object is the module of vector fields tangent to the arrangement, called the module of logarithmic derivations, which was introduced by Saito in 1980 to study the singularities of hypersurfaces. An enduring mystery in the theory of hyperplane arrangements is which algebraic properties of the module of logarithmic derivations can be determined from the intersection lattice, and which properties depend fundamentally on the geometry (i.e. the exact hyperplanes). At the center of this mystery is Terao's conjecture, which proposes that the algebraic property of freeness can be determined only from the intersection lattice. In this talk we explain how rigidity of planar frameworks (dating back to Maxwell) plays a key role in connecting the geometry and algebra of line arrangements in the projective plane. 
January 18 
Speaker: Timothy Rainone, Occidental College Title: Paradoxical decompositions, dichotomy, and FiniteApproximability in Operator Algebras Abstract: Notions of finiteness are prevalent in mathematics, not least in operator algebras. For instance, with matrix algebras we observe Dedekindfiniteness; that is every isometry is unitary. This also holds for large classes of C*algebras as well as their stabilization. Such algebras are called stably finite. At the opposite end of the spectrum are the purely infinite C*algebras whose internal structure admit paradoxical decompositions; especially when the algebras in question are crossedproduct constructions. In this talk we will study the stably finite/purely infinite dichotomy for certain C*algebras that arise from dynamical systems. We will then move our discussion to matricial field (MF) C*algebras; a subclass of stably finite algebras that admit external matrix approximations. The C*analogue of the Connes Embedding Conjecture proposes that every stably finite C*algebra should admit such an approximation. We show that is is indeed the case for large classes of crossed products of nuclear algebras by free groups. This talk is aimed at a general math audience; we will carefully introduce the theory of C*algebras as well as all the notions alluded to above. 
January 16 
Speaker: Alessandra Costantini, Oklahoma State University Title: Rees Algebras: An Algebraic Tool to Study Singularities Abstract: How many tangent lines does a plane curve have at a given point? And how can we effectively solve polynomial equations with integral coefficients? These seemingly unrelated problems from algebraic geometry and number theory can be both solved using tools from abstract algebra, through the notion of Rees algebras. 
January 13 
Speaker: Sudan Xing, University of Alberta, Canada Title: Dual OrliczMinkowski Problem Abstract: The classical Minkowski problem is a central problem in convex geometry which asks that given a nonzero finite Borel measure, what are the necessary and sufficient conditions on this measure such that it equals to the surface area measure of a convex body. In this talk, I will present the general dual extension of the classical Minkowski problem—the generalized dual OrliczMinkowski problem. 