# GSCAGT

#### June 2-3, 2018

This conference aims to expose graduate students in algebra, geometry, and topology to current research, and provide them with an opportunity to present and discuss their own research. It also intends to provide a forum for graduate students to engage with each other as well as expert faculty members in their areas of research. Most of the talks at the conference will be given by graduate students, with four given by distinguished keynote speakers.

This event is sponsored by the Department of Mathematics at Temple University and is pending sponsorship from the NSF.

View the conference poster here.

### Keynote Speakers

• #### Daniel Krashen   (University of Georgia)

• Title: Some Topological Viewpoints on Algebraic Structures
• Abstract: Understanding algebraic structures such as Galois extensions, quadratic forms and division algebras, can give important insights into the arithmetic of fields. In this talk, I will discuss recent work showing ways in which the arithmetic of certain fields can be partially described by topological information. I will then describe how these observations lead to arithmetic versions of the Meyer-Vietoris sequences, the Seifert–van Kampen theorem, and examples and counterexamples to local-global principles.
• #### Jean-François Lafont   (Ohio State University)

• Title: An introduction to K-theory and the isomorphism conjectures
• Abstract: I will give an overview of algebraic and topological K-theory of groups, focusing on three basic questions -- what these functors are, why we should care, and how can we compute them? We will start with some basic algebra, pass through some topology, and culminate with a discussion of the Farrell-Jones Isomorphism Conjectures and the Baum-Connes Conjecture.
• #### Kathryn Mann   (Brown University)

• Title: Foliated bundles, boundary actions, and rigidity
• Abstract: Take a surface $S$ of genus at least two, and consider the following three examples of actions of its fundamental group on the circle:
1. Put a hyperbolic metric on $S$. Then its fundamental group is a discrete subgroup of the group of isometries of hyperbolic space — $\text{PSL}(2,R)$ — which acts on the circle by Mobius transformations.
2. Using an idea of Gromov, the Cayley graph of $\pi_1(S)$ is itself hyperbolic (as a metric space), and admits a natural compactification by adding a circle to it. The action of the group on its Cayley graph extends to an action by homeomorphisms on this circle.
3. Look at geodesic flow on the unit tangent bundle $UTS$ of the surface. At each point of $UTS$ (classically, but non-obviously) there is a 2-dimensional subspace of the tangent space on which the flow is non-expanding. These integrate to form a foliation, and the holonomy of this foliation is an action of the fundamental group of the surface on the circle.
In this talk I’ll explain how these three things (all classical) are actually all the same thing — and then add a fourth description that comes from recent work of mine together with M. Wolff, as well as J. Bowden, S. Matsumoto, and others; with lots of suggestions for directions of future research.
• #### Helen Wong   (Carleton College)

• Title: Quantum topology, Hyperbolic geometry, and the Kauffman bracket skein algebra of a surface
• Abstract: The end of the previous century saw radical changes to three-dimensional topology, which arose from two completely different approaches. One breakthrough came from Thurston's introduction of hyperbolic geometry into the field. The second one came from the discovery of new quantum invariants for knots and three-dimensional manifolds, and brought in insight and techniques from mathematical physics and quantum groups. It is widely believed that the two approaches are intricately related, but there are few, well-understood points of connection. In this talk, we will focus on the Kauffman bracket skein algebra of a surface, and survey results that tie it to both quantum topology and hyperbolic geometry.

### Student Talks

In addition to the keynote speakers above, the weekend will be filled with 30-minute graduate student presentations. These talks may be expository or on original research, and will help graduate students share and learn exciting mathematics in the subjects of algebra, geometry, and topology.

## Logistics

### Conference Venue

All talks will be held in SERC (The Science Education and Research Center), located at 1915 N 12th St. For location and parking information see the campus map.

### Accommodations

We will be providing participant housing at Morgan Hall on campus. Note that there will be limited access to WiFi in the rooms. There is WiFi at local coffee shops etc., and eduroam is available on campus, but no additional WiFi is available at Morgan Hall.

### Getting to Temple by mass transit

SEPTA is the public transportation authority in Philadelphia. They run all the trains, buses, subways, etc. If you are local and have a SEPTA KEY card, we will reimburse your trips to and from the conference.

Follow signs for 'Ground Transportation' and then 'Trains to Center City'. You may purchase a ticket from the conductor on the train for \$8 (cash only) or you may purchase a "SEPTA Key Quick Trip" from the fare kiosks on the train platform for \$6.75 prior to boarding. Get on any train and get off at 'Temple University station' (all trains from the airport will stop here).

• #### From 30th Street Station:

Buy a ticket at one of the ticket counters; tell them you're trying to get to Temple University. Then take one of the following 'Regional Rail' lines and get off at the Temple stop: Chestnut Hill East, Fox Chase, Lansdale/Doylestown, Manayunk/Norristown, Warminster, West Trenton. One quick way to see which line is going to leave for Temple next is using Google maps.

## Schedule

A more detailed schedule is available here. Breakfast and lunch on both Saturday and Sunday will be provided.

### Saturday, June 2

Time Event
8:50am-9:30am Registration & Breakfast
9:30am-9:40am Opening Remarks
9:40am-10:40am Kathryn Mann
11:10am-1:00pm Graduate student talks (block #1)
1:00pm-2:20pm Lunch
2:20pm-4:10pm Graduate student talks (block #2)
4:30pm-5:30pm Daniel Krashen
7:00pm-9:00pm Conference Banquet

### Sunday, June 3

Time Event
8:50am-9:20am Breakfast
9:20am-10:20am Jean-François Lafont
10:30am-11:40pm Graduate student talks (block #3)
12:00pm-1:00pm Helen Wong
1:00pm-2:20pm Lunch

## Registration

Note: Registration is currently closed.

## Title/Abstract Submission

Note: Abstract submission is currently closed.

## Archive

### Websites From Past Years

The following websites include lists of participants and titles/abstracts of talks: