Past Redbud Conferences

Dates and Speakers:

• 9/15 Michael Shumate, University of Arkansas
• 10/6 Josh Pankau, University of Oklahoma
• 10/27 Neil Hoffman, Oklahoma State University
• 11/17 Jonathon Johnson, Oklahoma State University
• 12/10 Peter Patzt, University of Oklahoma

Titles and Abstracts:

• Michael Shumate, University of Arkansas

• Title: Grid invariants for singular Legendrian links
• Abstract: If Λ₁ and Λ₂ are two oriented singular Legendrian links that are Legendrian isotopic, we first construct allowable front diagram representations of Λ₁ and Λ₂. These allowable front diagram have naturally associated singular grid diagram representatives G₁ and G₂, which can be related by a sequence of singular grid moves. The Legendrian invariants, λ⁺ and λ^-, in the nonsingular grid homology theory have a natural extension to the singular grid homology theory, and are natural under the newly defined singular grid moves. This construction gives two invariants of singular Legendrian links.

• Josh Pankau, University of Oklahoma

• Title: Pseudo-Anosov stretch factors coming From Thurston's construction
• Abstract: The Nielsen–Thurston classification of mapping classes tells us that, up to isotopy, every automorphism of a closed orientable surface S is either periodic, reducible, or pseudo-Anosov. The latter case has led to a rich theory with applications in (among others) dynamical systems, number theory, and low dimensional topology. Associated to every pseudo-Anosov mapping class f is a real number λ, called the stretch factor of f. Fried proved that every stretch factor is a bi-Perron unit and conjectured that every bi-Perron unit has a power that is a stretch factor of some pseudo-Anosov homeomorphism. In this talk, I will discuss my work on showing that Fried's conjecture is true for the class of Salem numbers, as well as classifying, up to power, the stretch factors coming from a construction of pseudo-Anosov maps due to Thurston, known colloquially as Thurston's Construction.

• Neil Hoffman, Oklahoma State University

• Title: Recovering knot diagrams from triangulations
• Abstract: While the study of knots originated from manipulating knot diagrams, one can also study knots by analyzing their complements. In fact, Gordon and Luecke showed two knots are equivalent if and only if their complements are homeomorphic. There are well-known procedures for constructing a knot complement from a knot diagram. We will analyze the problem from the other perspective: constructing a knot diagram from a triangulated knot complement and describe an algorithm to produce such a diagram with an eye towards the specific challenges associated to implementing it. This is joint work Robert Haraway, Saul Schleimer and Eric Sedgwick.

• Jonathon Johnson, Oklahoma State University

• Title: Bi-orderability and pretzel knots
• Abstract: The orderability of 3–manifold groups has become a topic of interest in the last couple of decades. For example, the L–space conjecture posits a surprising relationship between the left-orderability of the fundamental group of a rational homology sphere, the foliations of that manifold, and the manifold's Heegaard Floer homology. However, the fundamental groups of 3–manifolds with positive first Betti number are always left-orderable. In particular, knot groups are left-orderable. In this situation, bi-orderability is more illuminating. In this talk, I will discuss how a technique developed by Mayland can be used to study the bi-orderability of genus one pretzel knot groups.

• Peter Patzt, University of Oklahoma

• • Title: The Steinberg module in algebraic topology
  • Abstract: In this talk, I will give an introduction to the applications of the Steinberg module in algebraic topology. The Steinberg module was first introduced in representation theory but later Solomon and Tits discovered a geometric description as the top homology of the Tits building. It has many applications in algebraic topology and I want to highlight a few of them. Borel and Serre found it to be the virtual dualizing module of arithmetic groups. It comes up in spectral sequences Introduced by Quillen and by Rognes that compute algebraic K–theory. And it is recently used to improve ranges of the homological stability of general linear groups in the framework of Galatius, Kupers, and Randal-Williams. This talk includes joint works with Benjamin Brück, Alexander Kupers, Jeremy Miller, Rohit Nagpal, Andrew Putman, Robin Sroka, and Jennifer Wilson.

Organizers: Matthew Clay*, Max Forester, Neil Hoffman, Yo'av Rieck*, Henry Segerman, Jing Tao.
(*local organizers)

Questions or comments? Please contact Matthew Clay.

Updated: Tue 07 Dec 2021 09:15:27 AM CST

Redbud Fall 2017 Topology Conference

April 27-29, 2017
Reynolds Center on Campus
University of Arkansas at Fayetteville

The Redbud Topology conference is a regional conference in topology and related areas, with participants from the University of Arkansas, the University of Oklahoma, Oklahoma State University, and elsewhere. The conference will run all day Friday and all morning on Saturday, ending by 1 PM. There will also be a session on Thursday afternoon as a warm-up for graduate students. There will be dinner outing on Friday evening.

Speakers:

Hannah Alpert, (Brown University)
Khalid Bou-Rabee, (The City College of New York)
Moon Duchin, (Tufts University)
Mark Feighn, (Rutgers University-Newark)
Vincent Guirardel, (Université de Rennes 1)
Ilya Kapovich, (University of Illinois at Urbana-Champaign)
Priyam Patel, (University of California at Santa Barbara)
Kasra Rafi, (University of Toronto)
Andrew Sale, (Vanderbilt University)
Sam Taylor, (Yale University)

Schedule: The full schedule and talk abstracts are 

Register: We encourage participants to register so that we will have a head-count for the event. We expect to have some funds available to reimburse participant expenses. Priority will be given to registrations received prior to March 27.

Inclusiveness: The Redbud Topology Conference is supported by the University of Arkansas, the University of Oklahoma, Oklahoma State University and the National Science Foundation. As scholars representing these institutions, we pay special attention to their firm commitments to equal opportunity and diversity. In order to uphold these ideals, we strive to make each Redbud Conference an inclusive event and will not tolerate discrimination based on race, color, religion, national origin, sex (including gender identity, sexual orientation, and pregnancy), age, disability, genetic information or parental status. As part of this mission, the organizers are happy to provide details of local childcare options and lactation rooms for nursing mothers upon request.

Further information on the commitment to inclusiveness held by each institution can be found here:

The National Science Foundation's post award requirements

The University of Arkansas's equal opportunity statement

The University of Oklahoma's equal opportunity statement

Oklahoma State University's equal opportunity statement

Sponsors: Participant support is generously provided by the NSF award DMS-1702102 and in part by the Department of Mathematical Sciences at the University of Arkansas.

Organizers: Matt Clay*, Matt Day*, Max Forester, Neil Hoffman, Yo'av Rieck*, Henry Segerman, Jing Tao. 
(*local organizers)

Questions or comments? Please contact Matt Clay.

Redbud 2014 Fall Conference

November 1, 2014
University of Arkansas
SCEN 408

This is a regional conference in topology, broadly interpreted.
9:00 a.m. to 4:45 p.m.

Speakers

Thomas Church, Stanford University

Matt Day, University of Arkansas

Matthew Durham, University of Michigan

Robert Tang, University of Oklahoma

Pengcheng Xu, Oklahoma State University

Participant support provided by NSF award DMS-1419391.

Questions or comments? Please contact Matt Clay.

Organizers: Matt Clay, Matt Day, Yo'av Reick, Jeremy Van Horn-Morris

The Redbud Topology conference is a regional conference in topology and related areas, with participants from the University of Arkansas, the University of Oklahoma, Oklahoma State University, and elsewhere.

Redbud Conference

March 8, 2013

Schedule of Events

Graduate Workshop - Friday, March 8

SCEN 322
John Etnyre and Gordana Matic

workshop - 8:30 a.m. to noon (with breaks)
lunch - noon to 1:30 p.m. 
workshop - 1:30 p.m. to 5 p.m. (with breaks)

Saturday, March 9

SCEN 408

Matt Hedden - 9 a.m. to 10 a.m. 
(30 minute break)
Elena Pavalescu - 10:30 a.m. to 11:30 a.m.
Lunch - 11:30 a.m. to 1:30 p.m.
John Etnyre - 1:30 p.m. to 2:30 p.m.
(30 minute break)
Josh Sabloff - 3 p.m. to 4 p.m.
(30 minute break)
Lisa Traynor - 4:30 p.m. to 5:30 p.m.

Sunday, March 10

Dan Rutherford - 9:30 a.m. to 10:30 a.m.
(30 minute break)
Shea Vela-Vick - 11 a.m. to noon 

Optional afternoon trip to Crystal Bridges Museum of American Art, Bentonville 

Speakers

John Etnyre (Georgia Tech)
Title: Contact structures on 5 manifolds

Abstract: Contact structures, especially in dimension 3, have been studied extensively for quite some time but we still do not know which odd dimensional manifolds support such structures. In this talk I will discuss the proof that all almost contact 5 manifolds do admit contact structures.

Matt Hedden (Michigan State)
Title: Some recent progress on topologically slice knots

Abstract: Modulo a 4-dimensional equivalence relation, the set of knots in the 3-sphere can be endowed with
a group structure. The resulting group is called the concordance group and, perhaps surprisingly, the group depends on whether we work with homeomorphisms or diffeomorphisms. Particularly important to understanding this distinction is the set of topologically slice knots: those knots which bound topologically flat embedded disks in the 4-ball. I'll give an introduction and overview of the subgroup of concordance generated by topologically slice knots, and discuss recent work which provides the first examples of (two-) torsion elements in this subgroup. The new results which I'll mention are joint work with Se-Goo Kim and Charles Livingston.

Elena Pavelescu (Oklahoma State)
Title: Invariants of Legendrian graphs

Abstract: A Legendrian graph is a graph embedded in such a way that its edges are everywhere tangent to the contact structure. We first extend the classical invariants Thurston-Bennequin number and rotation number to Legendrian graphs as the ordered set of tb's and rot's taken over the set of cycles of the graph. We show that  graph G can be Legendrian realized with all cycles unknots of maximal tb=-1 if and only if G doesn't contain K_4 as a minor. We find all pairs (tb, rot) that can be realized as the invariants of a Legendrian theta-graph and we investigate how good is a pair (tb, rot) at distinguishing the Legendrian type of a graph. This is joint work with Danielle O'Donnol.

Dan Ruthorford (University of Arkansas)
Title and abstract: TBA


Joshua Sabloff (Haverford College)
Title: Geography of Legendrian Submanifolds

Abstract: I will discuss the structure of the space of Legendrian submanifolds in the standard contact R^{2n+1}, especially for n at least 2. The first lens I will use is geography, i.e. a survey of which sets of invariants can be realized by Legendrian submanifolds Using a construction involving embedded Legendrian surgery. I will examine the geography question for the non-classical generating family homology invariant and will show that optimal results can be achieved (this is joint work with Lisa Traynor and Frederic Bourgeois). The second lens is that of homotopy, and I will extend the examples used in the analysis of the geography question to construct loops of Legendrian spheres that are non-contractible in the space of Legendrians but are contractible in the smooth category (this is joint work with Mike Sullivan).

Lisa Traynor (Bryn Mawr College)
Title: The Geography of Lagrangian Cobordisms

Abstract: In topology, cobordisms define a fundamental equivalence relation on the set of compact manifolds: two compact, n-dimensional manifolds are cobordant if their disjoint union is the boundary of a (n+1)-dimensional manifold. I will discuss cobordisms that satisfy extra geometrical conditions imposed by symplectic and contact structures. Namely, I will discuss Lagrangian cobordisms between Legendrian manifolds. In contrast to the smooth setting, this cobordism relation no longer defines an equivalence relation on the set of Legendrian submanifolds. There are numerous interesting “geography” questions about the existence of Lagrangian cobordisms. I will discuss some obstructions to and constructions of Lagrangian cobordisms that give some geographic information.

Shea Vela-Vick (LSU)
Title: Transverse knots, infinite cyclic covers and Heegaard Floer homology.

Abstract: In recent years, Heegaard Floer theory has proven an invaluable tool for studying contact manifolds and the Legendrian and transverse knots they contain. I plan to discuss a method for defining a variant of Heegaard Floer theory for infinite cyclic covers of transverse knots in the standard contact 3-sphere. This invariant takes the form of a Z[t,t^-1]-module and generalizes one defined in joint work with Baldwin and Vertesi for transverse knots braided about open book decompositions. In this talk, I will discuss how our invariant is constructed and present some basic properties. This is joint work with Tye Lidman and Sucharit Sarkar.

Graduate Workshop

Friday, March 8 

John Etnyre (Georgia Institute of Technology) and Gordana Matic (University of Georgia).

1. Etnyre-Contact and almost contact manifolds Abstract: Contact geometry is a venerable subject that arose in various concrete situations such as celestial mechanics and thermodynamics. In the last few decades they have been much studied and been shown to have surprising connections to many areas of mathematics. In this talk I will introduce contact structures on manifolds and discuss "obvious" properties a manifold must have to admit a contact structure. 

2. Matic-Contact topology, convex surfaces and open books. 

3. Etnyre-Legendrian knot theory. 

4. Matic-Contact topology and Heegaard Floer Homology

All are welcome to attend. If you'd like to participate, plan on arriving on Thursday and let us know either by

November 3rd, 2012, University of Oklahoma, Nielsen Hall room 251.

This is a regional conference in topology, broadly interpreted. The target audience is mathematicians from the University of Arkansas, Oklahoma State University, and the University of Oklahoma.

The conference will run from 9:30 am to 4:15 pm, with coffee beforehand and dinner afterwards.

Speakers:

 

Matt Day, University of Arkansas

 

Funda Gultepe, University of Oklahoma

 

Dale Rolfsen, University of British Columbia

 

Jeremy Van Horn-Morris, University of Arkansas

We encourage participants to register so that we will have a head-count for the event. Please register by Thursday October 18 if at all possible. We have some funds available to reimburse participant expenses. To be considered for support, please register.

Location, hotel and travel information can be found here.

A map showing various items of interest can be found here.

Questions or comments? Please contact Max Forester (forester@math.ou.edu).

Updated October 30th, 2012.

November 19th, 2011, University of Arkansas, SCEN building room 408.

This is a regional conference in topology, broadly interpreted. The target audience is mathematicians from the University of Arkansas, Oklahoma State University, and the University of Oklahoma.

The conference will run from 9:30 am-4:15 pm. There will be dinner afterwards.

Speakers:

Matt Clay, Allegheny University

Jesse Johnson, Oklahoma State

Joel Louwsma, University of Oklahoma

Dan Rutherford, University of Arkansas

We encourage participants to register so that we will have a head-count for the event. We expect to have some funds available to reimburse participant expenses (NSF support is pending). To be considered for support, please register.

Location, hotel and travel information can be found here.

Questions or comments? Please contact Matt Day (matthewd@uark.edu).

Updated November 12th, 2011.