Calendar
Fall 2023
September 8 
Speaker: Ross Staffeldt, NMSU In odd dimensions there are analogues of almost complex manifolds called K contact manifolds and analogues of complex manifolds called Sasakian manfolds. Since the cartesian product of odd dimensional manifolds is even dimensional, the product of Sasakian manifolds is replaced by a join construction that produces a 2m+2n+1 dimensional Sasakian manifold from Sasakian manifolds of dimensional 2m+1 and 2n+1. We are interested in eventually classifying up to homeomorphism or diffeomorphism the results of applying the join construction to a circle bundle over a closed surface of genus g and to a 3sphere with a weighted circle action. We will describe results of the first step in a classification, namely, the calculation of homotopy and homological invariants. Authors: Candelario Castaneda and Ross Staffeldt 
August 25 
Speaker: Prasit Bhattacharya, NMSU 
August 18 
Speaker: Elizabeth Gasparim 
Previous Seminars
Spring 2023
April 28 
Speaker: Inkang Kim, Korean Institute of Advanced studies, Seoul 
April 14 
Speaker: Franjo Šarčević (University of Sarajevo, Bosnia) Title: rImmersions from the Point of View of Functor Calculus 
April 7 
Speaker: Morgan Opie (University of California at Los Angeles Abstract: Given two complex topological bundles over $\mathbb CP^n$, one can ask whether the bundles are topologically equivalent. The first test is to compare their Chern classes, since equivalent bundles must have the same Chern data. The converse fails in general, which leads to the following question: given $n$ and $k$ positive integers, what invariants beyond Chern classes are needed to distinguish complex rank $k$ topological bundles on $\mathbb CP^n$, up to topological equivalence? 
March 3 
Speaker: Luis ValdezSanchez (University of Texas, El Paso In this talk we restrict our attention to genus one hyperbolic knots in the 3sphere. We will see that the number of `disjoint and nonparallel' Seifert tori bounded by such knots is at most 5 and discuss the construction of various examples of knots bounding maximal disjoint collections of Seifert tori. 
February 24 
Speaker: Urs Schreiber (New York University, Abu Dhabi

February 17 
Speaker: Julia Seminika, University of Muenster Title: Cutandpaste Invariants of Manifolds, Ktheory and Cobordisms Abstract: The generalized Hilbert’s third problem asks about the invariants preserved under the scissors congruence operation: given a polytope P in R^n, one can cut P into a finite number of smaller polytopes and reassemble these to form Q. Kreck, Neumann and Ossa introduced and studied an analogous notion of cutandpaste relation for manifolds called the SKequivalence ("schneiden und kleben" is German for "cut and paste"). 
February 3 
Speaker: Luca Pol (University of Regensberg Title: Quillen stratification in equivariant homotopy theory Abstract: Quillen’s celebrated stratification theorem provides a geometric description of the Zariski spectrum of the cohomology ring of any finite group with coefficients in a field in terms of information coming from its elementary abelian psubgroups. The goal of this talk is to discuss an extension of Quillen's result to the world of equivariant tensortriangular geometry. For the category of equivariant modules over a commutative equivariant ring spectrum we obtain a stratification result in the terms of the geometric fixed points equipped with their Weylgroup actions for all subgroups, and hence a classification of localizing tensor ideals. Finally, I will apply these methods to several examples of interests such as Borelequivariant Morava Etheory and equivariant topological Ktheory. This is joint work with Tobias Barthel, Natalia Castellana, Drew Heard and Niko Naumann. 
Fall 2022
November 18 
Speaker: Clover May, Norwegian University of Science and Technology

November 11 
Speaker: Foling Zou, University of Michigan 
November 4 
Speaker: Prasit Bhattacharya, New Mexico State University 
October 28 
Speaker: Tom Bachmann, University of Oslo, Germany 
October 21 
Speaker: Jerry Lodder, New Mexico State University 
October 14 
Speaker: Subhadip Dey Title: Discrete Subgroups of PU(2,1) with Large Critical Exponents Abstract: Let Γ be a discrete subgroup of PU(2,1), the isometry group of the complexhyperbolic space CH² of (complex) dimension two. Under a suitable normalization of the Riemannian metric of CH², the critical exponent δ(Γ) of Γ, when Γ is a lattice, is 4. In this talk, we discuss an example of a sequence (Γₙ) of discrete subgroups of PU(2,1) such that, for all n \in N, δ(Γ_n) < 4, but δ(Γ_n) → 4, as n → ∞. This example shows that Corlette’s gap theorem on critical exponents of discrete isometry groups of the quaternionichyperbolic spaces does not hold for CH². This talk is based on joint work with Beibei Liu. 
September 30 
Speaker: Ross Staffeldt, New Mexico State University Title: The Complex Projective Line and the Fundamental Group of the Circle (Part 2). Abstract: How are these things related? The concept of "line bundle" provides the link. After reviewing a few basic facts about projective spaces, we will explore the concept through examples. In particular, we will show how to attach elements of the fundamental group of the circle to the normal bundle of the projective line in the projective plane, the canonical bundle over the line, and, possibly, the tangent bundle of the line. 
September 23 
Speaker: Ted Stanford, New Mexico State University Title: Free Taylor Polynomials in Lowdimensional Topology Abstract: Taylor polynomials, sums of powers of (xa), are familiar objects incalculus. There exists an interesting noncommutative generalization ofthis technique to free groups, which turns out to be useful for analyzingvarious groups which arise frequently in lowdimensional topology, such as knotgroups, link groups, and braid groups. I will assume basic familiaritywith groups and rings. 
September 9 
Speaker: Ross Staffeldt, New Mexico State University Title: The Complex Projective Line and the Fundamental Group of the Circle Abstract: How are these things related? The concept of "line bundle" provides the link. After reviewing a few basic facts about projective spaces, we will explore the concept through examples. In particular, we will show how to attach elements of the fundamental group of the circle to the normal bundle of the projective line in the projective plane, the canonical bundle over the line, and, possibly, the tangent bundle of the line. 