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Holomorphic Differentials in Mathematics and Physics: February 4 – 8, 2019

Attendee List scheduleView Videos

Organized by Jayadev Athreya, Steve Bradlow, Sergei Gukov, Andy Neitzke, Anna Wienhard, and Anton Zorich
 

Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special – Hitchin or higher Teichmuller – components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).

It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our program will be of interest to those working in many different Fields, including low-dimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).  This workshop is associated with the program Geometry and Physics of Hitchin Systems: January 22 – June 21, 2019

Talk Schedule


Time Title Speaker Location
9:30am Discrete groups, Lyapunov exponents, and Hodge theory Simion Filip SCGP 102
10:30am Coffee break N/A SCGP Cafe
11:00am A combinatorial approach to saddle-counting invariants for quadratic differentials Pietro Longhi SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:15pm Compactifying moduli of curves with a differential Samuel Grushevsky SCGP 102
3:30pm Tea time N/A SGCP Cafe
4:00pm The monodromy of meromorphic projective structures Dylan Allegretti SCGP 102

Time Title Speaker Location
9:30am Stratifications and conformal limits Brian Collier SCGP 102
10:30am Coffee break N/A SCGP Cafe
11:00am Limiting Configurations, Pleated Surfaces and Harmonic Maps Michael Wolf SCGP 102
12:00pm Lunch N/A SCGP Cafe
1:00pm SCGP Weekly Talk: BPS states and hyperkahler metrics: an update Andrew Neitzke SCGP 102
2:15pm Variational Formulas for the Period Matrix and Shimura-Teichmuller Curves Chaya Norton SCGP 102
3:30pm Tea time N/A SGCP Cafe
4:00pm Meromorphic quadratic differentials and geometric structures Subhojoy Gupta SCGP 102

Time Title Speaker Location
9:30am Conformal blocks and Higgs bundles for spin groups Richard Wentworth SCGP 102
10:30am Coffee break N/A SCGP Cafe
11:00am Categorified Wall-Crossing With Twisted Masses Gregory Moore SCGP 102
12:00pm Lunch N/A SCGP Cafe
3:30pm Tea time N/A SGCP Cafe
6:00pm Banquet SCGP 102

Time Title Speaker Location
9:30am The elliptic orbifold of order 5 Philip Engel SCGP 102
10:30am Coffee break N/A SCGP Cafe
11:00am Volume and intersection theory on moduli spaces of holomorphic differentials Dawei Chen SCGP 102
12:00pm Lunch N/A SCGP Cafe
1:30pm Systolic inequality for K3 surfaces via stability conditions Yu-Wei Fan N/A
2:45pm A bumpy ride through the space of half-translation structures Aaron Fenyes N/A
3:45pm Tea time N/A SGCP Cafe
4:15pm TBA Michael Wolf SGCP 102

Time Title Speaker Location
9:30am Modular tensor categories from wild Higgs bundles Du Pei SCGP 102
10:30am Coffee break N/A SCGP Cafe
11:00am Geometric correspondances between singular fibres of the Hitchin fibration Laura Schaposnik SCGP 102
12:00pm Lunch N/A SCGP Cafe
3:30pm Tea time N/A SCGP Cafe