# GSCAGT

#### June 1-2, 2019

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 by the NSF.

### Keynote Speakers

• #### Dusa McDuff   (Barnard College)

• Title: Embedding problems in symplectic topology
• Abstract: The question of when one symplectic set (such as an ellipsoid or ball) embeds into another turns out to have very interesting answers, that exemplify the fine line between flexibility and rigidity that is so characteristic of symplectic topology. This will be a general introduction to the topic suitable for students who know some geometry/topology but nothing about symplectic geometry.
• The slides for this talk are now available here
• #### Mona Merling   (University of Pennsylvania)

• Title: Algebraic K-theory and group actions
• Abstract: Quillen’s algebraic K-theory of rings has deep connections to problems in number theory, and Waldhausen's A-theory, an extension of algebraic K-theory to spaces, is central to the classification of diffeomorphisms of manifolds. I will give a description of this exciting subject and some of the problems it relates to, and I will discuss current work on equivariant algebraic K-theory.
• #### Priyam Patel   (University of California, Santa Barbara)

• Title: Mapping class groups of infinite-type surfaces and their actions on hyperbolic graphs
• Abstract: Given a finite-type surface, there are two important objects naturally associated to it. The first is the mapping class group: the group of homeomorphisms of the surface up to isotopy (a natural equivalence). The second is the curve graph: an infinite-diameter hyperbolic graph on which the mapping class group acts via isometries. This action is well understood and has been extremely useful in understanding the algebraic and geometric properties of mapping class groups. There has been a recent surge in studying surfaces of infinite type, i.e. with infinitely generated fundamental group, and in this talk we shift our focus to their mapping class groups. We first discuss the problem of choosing an appropriate graph for the mapping class group to act on in this setting, and then describe recent joint work with Carolyn Abbott and Nicholas Miller explicitly constructing infinite-type mapping classes with interesting (loxodromic) actions on this graph.
• #### Ravi Vakil   (Stanford University)

• Title: The space of vector bundles on spheres: algebra, geometry, topology
• Abstract: Bott periodicity relates vector bundles on a topological space $X$ to vector bundles on $X \times S^2$: the “moduli space” $BU$ of complex vector bundles is basically the same as the “moduli space” maps of a sphere to $BU$. I’m not a topologist, so I will try to explain an algebraic or geometric incarnation, in terms of vector bundles on the Riemann sphere. The algebro-geometric incarnation of Bott periodicity is actually motivated by important current questions in geometry. I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally. This is joint work in progress with Hannah Larson, who did the heavy lifting.

### 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.

• schedule of talks
• titles and abstracts

• ## 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.

There are two ways to get back to Temple from center city. The fare for either is $2.50. If you are on or near Broad Street, look for a subway station with a "Broad Street Line" sign. Take the Broad Street Line LOCAL North and get off at Cecil B. Moore station. Morgan Hall is on the southeast corner of Broad and Oxford, right where the subway station exit is. The other way is to take the 23 bus uptown, which you can catch at the corner of 11th and Market. Get off at 11th and Oxford, and walk west on Oxford (in the direction of traffic). Morgan Hall will be on your left. ### Parking at Temple There is a daily rate of$20 per entry in:

• the 15th Street Lot
• the Diamond Street Lot
• the Liacouras Garage
• the Norris Street Lot
An hourly rate of $4 is charged in: • the Cecil B. Moore Lot • the Montgomery Garage An hourly rate of$6 is charged in the Tuttleman Lot.

### Conference Banquet

There will be a banquet Saturday night open to all participants.

• Assorted vegetable and tofu soup (VV, GF, LF)
• Walnut shrimp (LF)
• Saute sugar snap pea, bamboo shoot, mushroom, and lotus root (VV, GF, LF)
• Snowpea shoots in garlic sauce (VV, GF, LF)
• Buddist stewed crispy tofu (VV, LF)
• Crispy roasted chicken (GF, LF)
• Braised fish casserole (LF)
• Mushroom E-fu noodles (VV, LF)
• Vegetarian friend rice (V, GF, LF)

Tags: VV-vegan, V-vegetarian, GF-gluten-free, LF-lactose-free, P-pescatarian

If you plan on attending the banquet, please bring \$10 when you register on Saturday morning. If you wish to bring guests, bring \$20 for each guest. From the conference venue, you can get to the restaurant either by subway (Broad Street Line) or bus (route 23). --> For the subway, get off at Race-Vine. For the bus, get off at Race St.

## Schedule

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

### Saturday, June 1

Time Event
8:50am-9:30am Registration & Breakfast
9:30am-9:40am Opening Remarks
9:40am-10:40am Ravi Vakil
10:40am-11:10am Coffee/Tea Break
11:10am-1:00pm Graduate student talks (block #1)
1:00pm-2:20pm Lunch
2:20pm-4:10pm Graduate student talks (block #2)
4:10am-4:30am Coffee/Tea Break
4:30pm-5:30pm Priyam Patel
7:00pm-9:00pm Conference Banquet

### Sunday, June 2

Time Event
8:30am-9:00am Breakfast
9:00am-10:00am Mona Merling
10:00am-10:20am Coffee/Tea Break
10:20am-12:10pm Graduate student talks (block #3)
12:10am-12:30am Coffee/Tea Break
12:30pm-1:30pm Dusa McDuff
1:30pm-2:30pm Lunch

## Registration

Note: Registration is now closed. The deadline for funding is Friday, April 12th, 2019. There is no registration fee. Members of gender, racial, and ethnic groups underrepresented in mathematics are encouraged to apply.

## Title/Abstract Submission

Note: Abstract submission is now closed.

## Archive

### Websites From Past Years

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