### About

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 NSF and the Department of Mathematics at Temple University.

View the conference poster.

### Keynote Speakers

• #### Renato Bettiol   (University of Pennsylvania)

• Title: Deforming flat manifolds and flat orbifolds
• Abstract: Flat orbifolds (respectively, manifolds) are quotients of Euclidean space by crystallographic groups (respectively, torsion-free crystallographic groups). For example, in dimension 2, there are 17 distinct flat orbifolds corresponding to the 17 wallpaper groups, out of which only 2 are manifolds: the 2-torus and the Klein bottle. In this talk, I will explain the basic structure of these objects and describe the moduli space of flat metrics on them, showing that flat manifolds can always be deformed, while flat orbifolds may be rigid. I will also describe the boundary of the moduli space; showing that limits of flat manifolds are flat orbifolds and, conversely, that every flat orbifold is the limit of flat manifolds. This is joint work with Andrzej Derdzinski and Paolo Piccione.
• #### Spencer Dowdall   (Vanderbilt University)

• Title: Hyperbolic geometry in group extensions
• Abstract: I will introduce some basic concepts of geometric group theory by exploring the theme of coarse negative curvature in group extensions. After giving the definition of (Gromov) hyperbolic groups and presenting a few remarkable consequences, we'll look at group extensions and consider when they may be hyperbolic. The geometry of a group extension turns out to be tied up in the action of the quotient group (of the extension) on the kernel by outer automorphisms. Examining this outer action will naturally lead us to certain parameter spaces for the kernel, such as the Teichmüller space, curve complex, Outer space, and free factor complex. With this setup I'll describe results of Farb-Mosher, Kent-Leininger, and Hamenstädt characterizing hyperbolic extensions of surface groups, as well as joint work with Taylor on hyperbolicity of free group extensions.
• #### Holly Krieger   (University of Cambridge)

• Title: Unlikely intersections in complex dynamics
• Abstract: I will discuss the philosophy of unlikely intersections in arithmetic and algebraic geometry, and the application of this philosophy to algebraic dynamical systems. I'll focus on the use of dynamical heights and study as an example the dynamical André-Oort conjecture, resolved in joint work with Ghioca, Nguyen, and Tucker.
• #### Emily Peters   (Loyola University Chicago)

• Title: Proof by pictures
• Abstract: Maybe you've heard of diagram algebras, planar algebras, spiders or something similar. And you're wondering, is this really math? Are the pictures an analogy or are they actual mathematical objects? Happily, there are rigorous mathematical frameworks that have pictures as their ingredients. I'll tell you about some of the most exciting examples, including the Temperley-Lieb algebra (and its relation to knot theory), the color-counting planar algebra (and the five-color theorem), and the extended Haagerup subfactor (joint work with Bigelow, Morrison and Snyder).

### 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. A preliminary schedule of talks is available here.

## Logistics

### Conference Venue

All talks will be held in SERC, 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. More details to follow...

### Getting to Temple by mass transit

SEPTA is the public transportation authority in Philadelphia. They run all the trains, buses, subways, etc.

### Conference Banquet

There will be a banquet Saturday night at Ocean Harbor. Here's the menu (v denotes the meal is vegetarian):

• Tofu and vegetable soup (v)
• Vegetarian spring roll (v)
• Walnut shrimp
• Asparagus with bamboo shoots (v)
• Snowpea spouts with garlic (v)
• Crispy fried chicken
• Chinese okra (sheng squash) and mushrooms (v)
• Pan seared flounder
• Vegetarian fried rice (v)

If you plan on attending the banquet, please bring \$10 when you register on Saturday morning. You will receive two tokens, which can be used Saturday night to get to the restaurant and back. They can be used either for the subway (Broad Street Line) or the bus (route 23). For the subway, get of at Race-Vine. For the bus, get off at Race St.

## Schedule

A more detailed schedule is available here. Note: This schedule is tentative.

### Saturday, June 3

Time Event
8:30am-9:10am Registration
9:10am-9:20am Opening remarks
9:20am-10:20am Plenary Speaker 1
10:50am-12:40pm Graduate student talks (block #1)
12:40pm-2:20pm Lunch
2:20pm-4:10pm Graduate student talks (block #2)
4:30pm-5:30pm Plenary Speaker 2
7:00pm-9:00pm Conference Banquet

### Sunday, June 4

Time Event
9:00am-10:50am Graduate student talks (block #3)
11:15am-12:15pm Plenary Speaker 3
12:15pm-1:40pm Lunch
1:40pm-2:50pm Graduate student talks (block #4)
3:00pm-4:00pm Plenary Speaker 4

## Registration

Note: The deadline for registration submission is May 11. However, we will give funding priority to participants who register by May 1.

## Title/Abstract Submission

Note: The deadline for title and abstract submission has passed. Abstracts received at this time might be accommodated via a waitlist, but we make no promises.

## Contact Us

If you have any questions or concerns do not hesitate to contact us at: templegscagt[at]temple[dot]edu