The seminar has talks on a variety of topics in topology, including algebraic geometry, chromatic homotopy theory, continuum theory, model categories, Nielsen fixed-point theory, simplicial sets, span theory, symmetric spectra, and topological groups.

For more information contact Daniel Davis.

Fridays at 1:00 in MDD 208

- No seminar due to the Mathematics Colloquium at 1:10.
**6 February 2015** - An overview of Bousfield localization for spectra
**13 February 2015**

**Time and location change due to holiday: 10:00 MDD 202**

Daniel Davis - Instead of a seminar, there is a Mathematics Colloquium in topology:
**20 February 2015**

Finite-type invariants and Taylor towers for spaces of knots and links

Robin Koytcheff (University of Victoria) - Part I: a little more on Bousfield localization; Part II: Lindner's paper on Mackey functors
**27 February 2015**

Daniel Davis - A 'Mackey functor' (which is a certain pair of functors) really is a functor!
**6 March 2015**

Daniel Davis - No seminar: The 2014 Lloyd Roeling Conference/2015 SRAC starts today.
**13 March 2015** - More on Mackey functors: finishing Lindner's theorem and the example for finite G-sets
**20 March 2015**

Daniel Davis - An Introduction to Sheaves
**27 March 2015**

Christopher Ryan

Abstract: The notion of a sheaf is introduced, and some basic properties of sheaves are given along with the origins and motivation of sheaf theory. - Motivic K-theory symmetric ring spectrum
**17 April 2015**

Youngsoo Kim (Tuskegee University)

The construction of a motivic symmetric ring spectrum representing algebraic K-theory will be presented. We will discuss the associativity of the multiplicative structure, and also discuss how it can be solved using standard vector bundles. - Modules and splittings
**24 April 2015**

Scott Bailey (Clayton State University)

Abstract: In this talk, we will discuss past, present, and future work in the classification of stable isomorphism classes of B-modules (where B is a sub-Hopf algebra of the Steenrod algebra). Past, present, and future applications to the splitting of the Tate spectra of v_n-periodic cohomology theories will also be discussed. - Resolutions of the $K(2)$-local sphere spectrum
**1 May 2015**

Irina Bobkova (University of Rochester)

Abstract: Computing the stable homotopy groups of spheres is a long-standing problem in algebraic topology. I will begin by introducing the subject of chromatic homotopy theory which describes the homotopy of the p-local sphere spectrum S through a family of localizations $L_{K(n)}S$ with respect to Morava K-theories $K(n)$. I will discuss computational tools which arise from the theory of formal group laws and their deformations. Then I will specialize to the $K(2)$-local category and talk about finite resolutions of the $K(2)$-local sphere spectrum by a sequence of spectra and some recent computations.

Fridays at 1:00 in MDD 208

- Cohomology: A Mirror of Homotopy
**19 September 2014**

Agnes Beaudry (University of Chicago)

Abstract: The philosophy of chromatic homotopy theory is that the stable homotopy groups of the sphere $S$ can be reassembled from the homotopy groups of a family of spectra $L_{K(n)}S$. Roughly, $L_{K(n)}S$ is the $n$-th chromatic layer of $S$. There are spectral sequences whose input is the cohomology of a group, the Morava Stabilizer group, and whose output is the homotopy of the $n$-th chromatic layer. In this talk, I will illustrate how some of these spectral sequences mirror the homotopy groups of $L_{K(n)}S$ and of $S$. - Model categories and the example of simplicial sets
**3 October 2014**

Daniel Davis - Model categories: some results and homotopy-theoretic maneuvers
**17 October 2014**

Daniel Davis - What is a simplicial category? A simplicial model category?
**31 October 2014**

Daniel Davis - Face maps, degeneracies, \Delta[3], and left homotopy
**7 November 2014**

Daniel Davis - A canonical presentation of an arbitrary simplicial set and the example of \Delta[2]
**14 November 2014**

Daniel Davis - Cofibrant objects, projectives, and left homotopy
**21 November 2014**

Daniel Davis

- Left homotopy in general and for simplicial sets, and Whitehead's theorem
**5 December 2014**

Daniel Davis

Fridays at 1:00 in MDD 208

- Bigraded modules, exact couples, and spectral sequences
**31 January 2014**

Daniel Davis - The tail of quantum spin networks
**7 February 2014**

Mustafa Hajij (graduate student, LSU)

Abstract: We study the tail, a q-power series invariant of a sequence of admissible trivalent graphs with edges colored n or 2n. We use local skein relations to understand and compute the tail of these graphs. For many quantum spin networks they turn out to be interesting number-theoretic q-series. In particular, certain quantum spin networks give a skein-theoretic proof for the Andrews-Gordon identities for the two-variable Ramanujan theta function as well to corresponding identities for the false theta function. Finally, we also give a product formula that the tail of such graphs satisfies. - A nugget in the tool chest of a working homotopy theorist: affine group schemes
**14 February 2014**

Daniel Davis

- The speaker originally scheduled for 14 February, Scott Bailey (Clayton State University), was not able to make it due to the ice storm in Atlanta. He had planned to speak on: Modules and splittings
**Note**

Abstract: In this talk, we will discuss past, present, and future work in the classification of stable isomorphism classes of B-modules (where B is a sub-Hopf algebra of the Steenrod algebra). Past, present, and future applications to the splitting of the Tate spectra of v_n-periodic cohomology theories will also be discussed. - Invariant contact structures on 7-dimensional nilmanifolds
**21 February 2014**

Sergii Kutsak (Florida Institute of Technology)

Abstract: I will give the list of all 7-dimensional nilpotent real Lie algebras that admit a contact structure. Based on this list, I will describe all 7-dimensional nilmanifolds that admit an invariant contact structure. Also I will give countably infinitely many examples of 7-dimensional nilmanifolds $N$ such that $N$ admits an invariant contact structure and $N \times S^1$ cannot admit a symplectic structure. - Vojislav Petrovic (graduate student)
**28 February 2014**

(**Note:**Due to the preparations for Mardi Gras, Voja's talk has been rescheduled for 2 May 2014.) - A computation in stable homotopy theory using topological modular forms
**7 March 2014**

Don Larson (Penn State Altoona)

Abstract: In this talk we will discuss a computation related to a very important object in stable homotopy theory known as the (3-primary) $K(2)$-local sphere. We will first put this computation in the context of a broader problem---namely, computing the stable homotopy groups of spheres---and then describe some surprising connections with classical number-theoretic objects like elliptic curves and modular forms. Finally, we will talk a bit about the computation itself. - Finite subgroups of a formal group of height 2 over F_9
**14 March 2014**

Yifei Zhu (Northwestern University)

Abstract: As an algebraic invariant attached to topological spaces, an elliptic cohomology theory records information about elliptic curves and integral modular forms. In particular, power operations in such a cohomology theory encode moduli problems of elliptic curves, specifically cyclic isogenies of the corresponding power. In this talk I'll discuss an explicit example. - Spaces of commuting elements in Lie groups
**21 March 2014**

Mentor Stafa (Tulane University)

Abstract: We study the spaces of commuting n-tuples in a compact and connected Lie group G, denoted Hom(Z^k,G). We introduce an infinite dimensional topological space denoted Comm(G), reminiscent of a Stiefel variety, that assembles the spaces Hom(Z^k,G) into a single space. This construction admits stable decompositions which allow the study of the spaces Hom(Z^k,G) and the Hilbert-Poincare series is also calculated using Molien's theorem. The cohomology of Comm(G) is given in terms of the tensor algebra generated by the reduced homology of the maximal torus. This is joint work with Fred Cohen. - Zariski's intrinsic description of nonsingular affine varieties
**28 March 2014**

Chris Ryan (University of Louisiana at Lafayette)

Abstract: This is an expository talk on the subject of classical algebraic geometry. We will look at a fundamental theorem of Zariski, which states that an affine variety is nonsingular at a point P if and only if the local ring of P on Y is a regular local ring. - Knot and link invariants for vector fields
**4 April 2014**

Rafal Komendarczyk (Tulane University)

Abstract: In 1979, V. I. Arnold showed that the fundamental invariant of 2--component links i.e. the linking number, can be generalized to an invariant of volume preserving vector fields. In this talk, the Arnold's construction will be outlined, as well as its various applications. Further, more recent results concerning generalizations of this construction to Vassiliev invariants of knots, will be discussed (joint work with Ismar Volic). - A Projective Model Structure on Pro-categories, and the Relative Étale Homotopy Type
**11 April 2014**

Tomer Schlank (M.I.T.)

Abstract: Isaksen showed that a proper model category $C$, induces a model structure on the pro-category $Pro(C)$. In this talk I will present a new method for defining a model structure on the pro-category $Pro(C)$. This method requires $C$ to satisfy a much weaker condition than having a model structure. The main application will be a novel model structure on pro-simplicial sheaves. We see that in this model structure a "topological lift" of Artin and Mazur's Étale homotopy type is naturally obtained as an application of some natural derived functor to the terminal object of the étale topos. This definition can be naturally generalized to a relative setting, namely, given a map of topoi T \to S, we get a notion of a relative homotopy type of T over S which is a Pro-simplicial object in S. This definition turns out to be useful for the study of rational points on algebraic varieties. This is a joint work with Ilan Barnea. - Derived functors of inverse limits and profinite G-modules
**2 May 2014**

Vojislav Petrovic (graduate student)

Fridays at 11:00 in MDD 311

- How do we regard a set of interesting morphisms in a category as being isomorphisms?
**13 September 2013**

Daniel Davis - The homotopy category of a homotopical category
**20 September 2013**

Daniel Davis - A presentation of the morphisms in a homotopy category by type
**27 September 2013**

Daniel Davis - A 3-arrow calculus for a homotopical category and saturation
**4 October 2013**

Daniel Davis - Boolean spaces
**18 October 2013**

Maciej Niebrzydowski - Representation theorems for Boolean algebras
**25 October 2013**

Maciej Niebrzydowski - A homotopical version of uniqueness in a category
**1 November 2013**

Daniel Davis - Lloyd Roeling Topology Conference
**8 November 2013** - On poset polynomials
**15 November 2013**

Maciej Niebrzydowski - Boolean quotients and Boolean derivatives
**22 November 2013**

Maciej Niebrzydowski - Continuous group cohomology of discrete G-modules and $\delta$-functors
**6 December 2013**

Vojislav Petrovic (graduate student)

Fridays at 1:00 in MDD 214

- An introduction to double categories
**1 February 2013**

Maciej Niebrzydowski - No seminar -- Mardi Gras break
**8 February 2013** - Symmetric spectra: the objects that give rise to generalized cohomology theories
**15 February 2013**

Daniel Davis - The symmetric monoidal category of symmetric spectra
**22 February 2013**

Daniel Davis - no seminar this week
**29 February 2013** - Symmetric spectra: some examples and the notion of stable equivalence
**8 March 2013**

Daniel Davis - The Temperley-Lieb category and its applications
**15 March 2013**

Maciej Niebrzydowski - On some models in statistical mechanics and their connections with topology
**22 March 2013**

Maciej Niebrzydowski - On n-ary algebras and their applications in knot theory
**12 April 2013**

Maciej Niebrzydowski - On stable equivalences and connective symmetric spectra
**19 April 2013**

Daniel Davis - Finite projective geometry
**26 April 2013**

Vic Schneider

Fridays at noon in MDD 214

- Entropic operations in knot theory
**7 September 2012**

Maciej Niebrzydowski - The Cuntz semigroup of low dimensional spaces
**14 September 2012**

Leonel Robert

Abstract: I will first define the Cuntz semigroup of a topological space (this object is of interest to C*-algebraists). I'll then describe the Cuntz semigroup for spaces of dimensions 0,1,2, and 3. - Progress on the "Hit Problem"
**21 September 2012 (ROOM CHANGE MDD 311)**

Shaun Ault (Valdosta State University)

- An introduction to nonabelian continuous cohomology
**28 September 2012**

Daniel Davis - A non-short, but not long, exact sequence in nonabelian continuous cohomology
**5 October 2012**

Daniel Davis - How does one build a Thom spectrum?
**19 October 2012**

Daniel Davis - An introduction to tolerance space theory
**26 October 2012**

Maciej Niebrzydowski - Finite geometries
**2 November 2012**

Vic Schneider - Bicomplex from degenerate elements of a weak simplicial module
**9 November 2012**

Jozef Przytycki (The George Washington University)

Abstract: Knot Theory motivated homology of quandles and racks, these in turn motivated the speaker to introduce distributive homology and to show that they can be described by a weak simplicial module. The degenerate part is not acyclic, however, it splits and its (right handed) filtration leads to a bicomplex, which is very approachable in the case of distributive homology. - Some remarks on differential groupoids
**16 November 2012**

Maciej Niebrzydowski - Finite geometries, part 2
**30 November 2012**

Vic Schneider

- Introduction to Haar integrals
**27 January 2012**

Vic Schneider - Introduction to Haar integrals, part 2
**3 February 2012**

Vic Schneider - The ends of groups
**10 February 2012**

Maciej Niebrzydowski - Ordered sets in combinatorics and topology
**17 February 2012**

Maciej Niebrzydowski - A discussion of inverse limits without a formal definition
**24 February 2012**

Brian Hill (graduate student) - NO SEMINAR
**2 March 2012**

- Lusternik-Schnirelmann theory - old and new
**9 March 2012**

Yuli Rudyak (University of Florida)

- A discussion of inverse limits without a formal definition, part 2
**16 March 2012**

Brian Hill (graduate student) - Ordered sets in combinatorics and topology, part 2
**23 March 2012**

Maciej Niebrzydowski - Tent maps and topological conjugacy
**30 March 2012**

Brian Hill (graduate student) - Pro-objects in a category and their morphisms
**20 April 2012**

Daniel Davis - Ordered sets in combinatorics and topology, part 3
**27 April 2012**

Maciej Niebrzydowski

- On some Cayley type theorems
**2 September 2011**

Maciej Niebrzydowski - On some Cayley type theorems, part 2
**9 September 2011**

Maciej Niebrzydowski - Selfcoincidences of Mappings between Spheres
**16 September 2011**

Duane Randall (Loyola University, New Orleans)

Abstract: The concepts of loose and also loose by small deformation are defined for mappings between spheres. The relationship in certain dimensions between mappings which are loose, but not loose by small deformation, with the existence or non-existence of Kervaire invariant one elements will be explained. - Discrete groups and manifolds in
**23 September 2011***S*^{2}x*R*

Jozsef Z. Farkas

Abstract: Thurston's geometrization conjecture played a crucial role for example in proving the Poincare conjecture. There are eight homogeneous simply connected geometries which give rise to compact three-manifolds. One of the simplest of the non-constant curvature ones is the space*S*^{2}x*R*, which as its name suggests, is the direct product of the sphere with the real line. Similarly to the "Euclidean strategy" we classify the crystallographic groups in*S*^{2}x*R*. We find 134 equivalence classes of space groups up to similarity. These in turn give rise to the 4 well-known compact manifolds admitting*S*^{2}x*R*geometry. - Obstruction theory for E_infty maps
**30 September 2011**

Niles Johnson (University of Georgia)

Abstract: We take an obstruction-theoretic approach to the question of algebraic structure on spectra. At its heart, this is an application of the Bousfield-Kan spectral sequence adapted for general operadic structure in a range of topological categories. This talk will focus on examples from rational homotopy theory which illustrate the obstructions to rigidifying homotopy algebra maps between differential graded algebras to strict algebra maps. In the topological context, these provide explicit examples of H_infty maps which cannot be rigidified to E_infty maps. - An introduction to operads and algebras over operads
**7 October 2011**

Daniel Davis

- Algebras over operads and some canonical examples
**14 October 2011**

Daniel Davis

**28 October 2011***S*^{2}x*R*space groups: generalized Coxeter groups and ball packings

Jozsef Farkas

- Fibered categories, fibers, and groupoids
**4 November 2011**

Daniel Davis

- Categories fibered in groupoids, monoids, and classifying spaces
**11 November 2011**

Daniel Davis

- Profinite Groups and Discrete G-Sets
**2 December 2011**

Brian Hill (graduate student)

Abstract: Some interactions between profinite groups and discrete G-sets will be explored. In addition, we will examine the sets of morphisms between discrete G-sets, as well as the Hom-set functor.

- Schubert polynomials and cohomology of flag manifolds
**19 January 2011**

Leonardo Mihalcea - Inverse limits with subsets of IxI
**26 January 2011**

Thelma West - Inverse limits with subsets of IxI, Part 2
**2 February 2011**

Thelma West - Inverse limits with subsets of IxI, Part 3
**16 February 2011**

Thelma West - Inverse limits of upper semi-continuous set valued functions
**23 February 2011**

Thelma West - Schubert varieties revisited
**2 March 2011**

Leonardo Mihalcea - Towards Schubert polynomials
**16 March 2011**

Leonardo Mihalcea - Towards Schubert polynomials, part 2
**23 March 2011**

Leonardo Mihalcea - Spatial graphs and their invariants
**30 March 2011**

Maciej Niebrzydowski - Areas of certain quadrilaterals
**6 April 2011**

Vic Schneider - Areas of certain quadrilaterals, part 2
**13 April 2011**

Vic Schneider - Continuous group cohomology for towers of discrete G-modules
**27 April 2011**

Daniel Davis

- Knotted surfaces
**17 September 2010**

Maciej Niebrzydowski - Knotted surfaces, part 2
**24 September 2010**

Maciej Niebrzydowski - A Tale of Six Atriodic Continua, Part 1
**8 October 2010**

Thelma West - No seminar this week due to the Roeling Conference.
**15 October 2010**

- A Tale of Six Atriodic Continua, Part 2
**22 October 2010**

Thelma West - postponed
**29 October 2010** - Introduction to inverse limits
**5 November 2010**

Thelma West - Quantum Schubert Calculus
**12 November 2010**

Leonardo Mihalcea

This will be a gentle introduction to main definitions and ideas of Schubert Calculus and its "quantum" version for Grassmannians. - An introduction to model categories
**19 November 2010**

Daniel Davis - An introduction to model categories, part 2
**3 December 2010**

Daniel Davis

- Kan complexes and categories
**January 29th:**

Daniel Davis - Kan complexes and $\infty$-categories
**February 5th:**

Daniel Davis - $\infty$-categories and composition through horns
**February 19th:**

Daniel Davis - Introduction to digital topology
**February 26th:**

Maciej Niebrzydowski - Axiomatic digital topology
**March 12th:**

Maciej Niebrzydowski - 'Composition' and joins for $\infty$-categories
**March 19th:**

Daniel Davis - Equivalent metrics and the spans of graphs, Part I
**March 26th:**

Thelma West - Equivalent metrics and the spans of graphs, Part II
**April 16th:**

Thelma West - Equivalent metrics and the spans of graphs, Part III
**April 23rd:**

Thelma West - $A^1$-Representability of Hermitian $K$-theory
**April 30th (ROOM 208):**

Girja Shanker Tripathi (graduate student, LSU)

Abstract: I will discuss my result that in the $A^1$-homotopy category of smooth schemes over a field of characteristic not equal to 2, the Hermitian $K$-theory is representable by "orthogonal Grassmannians." This result is the Hermitian analogue of the corresponding result for algebraic $K$-theory. I will introduce some ideas (parallel to the ones in topology) from the $A^1$-homotopy theory developed by Morel and Voevodsky (1999).

- Graph embeddings and chromatic numbers
**11 September 2009:**

Maciej Niebrzydowski - More on graph embeddings
**18 September 2009:**

Maciej Niebrzydowski - Sheaves of sets on a Grothendieck site
**25 September 2009:**

Daniel Davis - Limits and sheaves of sets on a site
**9 October 2009:**

Daniel Davis - Crossing numbers of graphs
**16 October 2009:**

Maciej Niebrzydowski - What is the Dimension of R(n)?
**23 October 2009:**

Roger Waggoner - Lloyd Roeling Conference
**30 October 2009:** - Representing graphs
**6 November 2009:**

Jake Sundberg (graduate student) - Representing graphs, part two
**13 November 2009:**

Jake Sundberg (graduate student) - Path connectedness
**20 November 2009:**

Vic Schneider - Path connectedness, part 2
**4 December 2009:**

Vic Schneider

- Introduction to span
**January 21st:**

Thelma West - Span, pt. II: a consideration of 'an atriodic tree-like continuum with positive span' (after Ingram)
**January 28th:**

Thelma West - Sheaves of abelian groups on topological spaces
**February 6th:**

Daniel Davis - Regular Sequences in unstable algebras over the Steenrod algebra
**February 13th:**

Mara Neusel (Texas Tech) - Connections between graph theory and knot theory
**February 20th:**

Maciej Niebrzydowski - Defining sheaves with equalizer diagrams and Grothendieck sites
**February 27th:**

Daniel Davis - Fibered products, sieves, and pretopologies on categories
**March 6th:**

Daniel - Connections between graph theory and knot theory, Part II
**March 13th:**

Maciej Niebrzydowski - Obtaining Grothendieck sites via bases
**March 20th:**

Daniel - Topological quandles
**March 27th:**

Maciej - Introduction to hyperspaces
**April 3rd:**

Thelma West - An Application of the snake and horseshoe lemmas to the functors Hom( - , G) and Ext( - , G), in the category
**April 24th:****Ab**

Chris Ryan (graduate student) - Size levels of arcs, continued
**May 1st:**

Thelma West

- Introduction to Khovanov homology I
**September 5:**

Maciej Niebrzydowski - No seminar due to Hurricane Ike
**September 12:** - Introduction to Khovanov homology II
**September 19:**

Maciej Niebrzydowski - Introduction to simplicial sets
**September 26:**

Daniel Davis - No seminar due to Fall break
**October 3:** - No seminar due to Hurricane Ike makeup classes
**October 10:** - Homotopy theory and simplicial sets
**October 17:**

Daniel Davis - Gram determinants in Knot Theory: skein module motivation
**October 24:**

Jozef Przytycki (The George Washington University) - The lattice of topologies on the set
**October 31:**

Vic Schneider - The lattice of topologies on the set, part 2
**November 7:**

Vic Schneider - No seminar
**November 14:** - Dimension theory 101
**November 21:**

Roger Waggoner - Elementary open problems in knot theory
**December 5:**

Maciej Niebrzydowski

- Inverse limits of spaces and their homotopy limits, with an eye on examples in continuum theory,
**January 28:**

Daniel Davis. - Beginning steps in understanding the relationship between algebraic geometry and complex-oriented cohomology theories,
**February 11:**

Daniel Davis. - Quandles, racks, and related knot invariants,
**February 18:**

Maciej Niebrzydowski. - Quandle homology theories and their connection with geometry of knots,
**February 25:**

Maciej Niebrzydowski. - Topological groups,
**March 3:**

Vic Schneider. - Topological groups, part two,
**March 10:**

Vic Schneider. - The homological algebra of the continuous cohomology of topological groups increases as one restricts to profinite groups,
**March 17:**

Daniel Davis. - Three basic examples employing inverse limits, Part I,
**March 31:**

Thelma West.

Inverse limits have appeared in various ways in the seminar, but no speaker has yet really dug into the interior of an inverse limit of topological spaces and really unpacked its meaning in a particular situation. One of the purposes of this talk (and the sequel on April 21st) is to give graduate students a better feel for inverse limits. - The Fixed Point Property,
**April 7:**

Roger Waggoner. - The Nielsen number,
**April 14:**

Roger Waggoner. - Three basic examples employing inverse limits, Part II,
**April 21:**

Thelma West. (This talk is a continuation of the March 31st seminar.) - Higher Grothendieck-Witt groups in Algebra and Topology,
**April 28:**

Marco Schlichting (Louisiana State University).

Abstract: I will motivate the study of higher Grothendieck-Witt groups (alias hermitian K-groups) of rings and schemes with two examples from topology-- cobordism categories of certain 4 manifolds (due to Giansiracusa) and an algebraic reinterpretation of 8-fold real Bott periodicity (due to Karoubi). Then I will explain a recent result of mine concerning the local-global behavior of those groups. - Part one: a brief statement of the definition of elliptic spectrum (related to Q(2) - from the last result of Daniel's colloquium)
**May 5:**

Daniel Davis, 5 minutes;

Part two: Elliptic curves, their associated abelian groups, and points of finite order,

Matthew Lennon (graduate student), a 25-minute talk;

Part three: The Nielsen number and the Jiang subgroup,

Roger Waggoner, a 35-minute talk.

contact us
Last updated 28 April 2015.

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