April 20, 2024 at Yale University

GATSBY is a conference organized by the geometry/topology groups at Brown and Yale. 

All are welcome! Please register. 

Principal Speaker

Schedule 

10-11:30 Reception (8th floor Kline Tower)

11:30-12:15 Background talk (Kline Tower 205)

12:15-2 Lunch (catered, 8th floor Kline Tower)

2-2:45 Lightning talks (Kline Tower 205)

2:45-3:30 Break

3:30-4:15 Research talk (Kline Tower 205)

4:15 Informal discussion followed by dinner for those interested

Abstracts

• Spencer Dowdall 

Background Talk: The coarse geometry of Teichmüller space and a new notion of complexity length

I will review the key features of Teichmüller space that are relevant to counting lattice points for the action of the mapping class group. Specifically, after introducing Teichmüller space I will discuss the thin regions and their inherent product structure. This will lead us to subsurface projections and Rafi's distance formula and associated combinatorial description of how Teichmüller geodesics pass through thin regions of subsurfaces. I will then introduce a new notion of "complexity length" in Teichmüller space that aims to carefully account for this motion of geodesics through product regions in a way that gives better control on the multiplicative errors and lends itself to counting problems.

Research Talk: Counting mapping classes by Nielsen-Thurston type

I will discuss the growth rate of the number of elements of the mapping class group of each Nielsen-Thurston type, that is, either finite-order, reducible, or pseudo-Anosov, measured via the number of lattice points in a ball of radius $R$ in Teichmüller space. For the whole mapping class group of the closed genus g surface, Athreya, Bufetov, Eskin, and Mirzakhani have shown this quantity is asymptotic to exp((6g-6)R) as R tends to infinity. Maher has obtained the same asymptotics for those orbit points that are translates by pseudo-Anosov elements. Obtaining a count for the finite-order or reducible elements is significantly more challenging due to the fact these non-generic subsets are not perceptible to the standard dynamical techniques. I will explain a naive heuristic for why the finite-order elements should grow at the rate of exp((3g-3)R), that is, with half the exponent. While this approach presents several obstacles, our new notion of complexity length provides the tools needed to make the argument work. Time permitting, I will also explain why the reducible elements grow coarsely at the rate of exp((6g-7)R). Joint work with Howard Masur.

• Lightning talks

Sam Freedman (Brown): Veech fibrations

Dongryul Kim (Yale): Nielsen-Thurston types and translation lengths of mapping classes along random walks

Tam Cheetham-West (Yale): Finite quotients of hyperbolic 3-manifold groups

Syantika Mondal (CUNY): Are these curves different?

Christa Ishimwe (Wesleyan): Octonions and exceptional Lie groups G_2 and F_4

Zhenghao Rao (Brown): Surface subgroups of cocompact lattices of isometries of hyperbolic spaces

Evan Scott (CUNY): A trisection picture for the involutions relating S^2⨉S^2, CP^2, and S^4

Junzhi Huang (Yale): Flows vs foliations: universal circles and ideal boundaries

Taro Shima (CUNY): Defining the quasi-conformal mapping class group

Local information

Locations below have free parking during the weekend.

Organizers:  Tam Cheetham-West, Subhadip Dey , Sam Freedman, Franco Vargas Pallete  and Bena Tshishiku

Previous iterations: Fall 2023, Spring 2023, Fall 2022, Spring 2019, Fall 2015, Spring  2015, Fall 2014, Spring 2014, Fall 2013,  Spring 2013, Spring 2012