Graduate Workshop on Moduli of Curves: July 7 – 18, 2014

Application for workshop is now closed.

Organized by Samuel Grushevsky, Robert Lazarsfeld, and Eduard Looijenga

Dates: July 7 – 18, 2014

Attendee ListDownload Talk ScheduleVideos

In recent years, moduli of Riemann surfaces (or algebraic curves) have come to play an increasingly central role in several fields of mathematics, including algebraic and complex geometry, topology, Teichmuller dynamics, mathematical physics, and even graph theory. But the very breadth of these applications has made it hard for students to develop a broad vision of the area. The purpose of this workshop is to introduce students to the moduli theory of Riemann surfaces simultaneously from the viewpoints of algebraic geometry, topology and Teichmuller theory.

The workshop will run for two weeks. The first will feature introductory lectures on the construction of the moduli space, both by using algebro-geometric techniques and via Teichmuller theory. In addition, two shorter courses will discuss concretely the moduli of n points on P^1, and the combinatorial perspective of tropical geometry. The second week will come closer to current research topics, including the birational geometry of the moduli space, the topology of surface bundles, and Teichmuller dynamics. Throughout the workshop, there will be a few one-time lectures on related developments.

With lecture courses by:

Benson Farb (University of Chicago): The geometry and topology of surface bundles
Gavril Farkas (Humboldt Universität): Birational geometry of moduli of curves
Maksym Fedorchuk (Boston College): GIT constructions of the moduli space of curves and its variants
Sam Payne (Yale University): Tropical curves
Jenia Tevelev (University of Massachusetts): Explicit moduli of n points on P^1
Scott Wolpert (University of Maryland): Construction of moduli space via Teichmuller theory
Alex Wright (University of Chicago): Teichmüller dynamics

and special lectures by:
Jeremy Kahn (CUNY)
Dennis Sullivan (Stony Brook/CUNY)

All workshop talks and problem sessions will be held in the Simons Center Lecture Hall (Room 102).

Tea time will either be in the Simons Center Lobby or on the patio outside of the Art Gallery (weather permitting).

Wednesdays, July 9th and 16th, are free afternoon days.

Graduate Workshop on Moduli of Curves Schedule

Time Title Presenters  Video
 8:30am Breakfast and registration begins (8:30am – 9:30am) SCGP Lobby and Cafe
 9:30am Construction of moduli space via Teichmuller theory (I) Scott Wolpert video
slides
10:45am Coffee Break SCGP Cafe
11:15am GIT constructions of the moduli space of curves and its variants (I) Maksym Fedorchuk video
12:30pm Lunch SCGP Cafe
 2:00pm Explicit moduli of n points on P^1 (I) Jenia Tevelev video
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Graduate participant talks (until about 5:00pm) Please see downloadable PDF for more information


Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Construction of moduli space via Teichmuller theory (II) Scott Wolpert video
slides
10:45am Coffee Break SCGP Cafe
11:15am GIT constructions of the moduli space of curves and its variants (II) Maksym Fedorchuk video
12:30pm Lunch SCGP Cafe
 2:00pm Explicit moduli of n points on P^1 (II) Jenia Tevelev video
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Problem session (until about 6:15pm)
 6:30pm The good pants homology and the Ehrenpreis conjecture Jeremy Kahn

Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Construction of moduli space via Teichmuller theory (III) Scott Wolpert video
slides
10:45am Coffee Break SCGP Cafe
11:15am GIT constructions of the moduli space of curves and its variants (III) Maksym Fedorchuk video
12:30pm Lunch SCGP Cafe
 3:30pm Tea Time SCGP Patio/Lobby

Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Construction of moduli space via Teichmuller theory (IV) Scott Wolpert video
slides
10:45am Coffee Break SCGP Cafe
11:15am GIT constructions of the moduli space of curves and its variants (IV) Maksym Fedorchuk video
12:30pm Lunch SCGP Cafe
 2:00pm Tropical curves (I) Sam Payne video
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Problem session (until about 6:15pm)

Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Construction of moduli space via Teichmuller theory (V) Scott Wolpert video
slides
10:45am Coffee Break SCGP Cafe
11:15am GIT constructions of the moduli space of curves and its variants (V) Maksym Fedorchuk video
12:30pm Lunch SCGP Cafe
 2:00pm Tropical curves (II) Sam Payne video
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Problem session (until about 6:15pm)

Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Teichmüller dynamics (I) Alex Wright video
10:45am Coffee Break SCGP Cafe
11:15am Birational geometry of moduli of curves (I) Gavril Farkas video
12:30pm Lunch SCGP Cafe
 2:00pm The geometry and topology of surface bundles (I) Benson Farb video
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Problem session (until about 6:15pm)  

Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Teichmüller dynamics (II) Alex Wright video
10:45am Coffee Break SCGP Cafe
11:15am Birational geometry of moduli of curves (II) Gavril Farkas video
12:30pm Lunch SCGP Cafe
 2:00pm The geometry and topology of surface bundles (II) Benson Farb video
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Problem session (until about 6:15pm)

Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Teichmüller dynamics (III) Alex Wright video
10:45am Coffee Break SCGP Cafe
11:15am The geometry and topology of surface bundles (III) Benson Farb video
12:30pm Lunch SCGP Cafe
 3:30pm Tea Time SCGP Patio/Lobby

Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Teichmüller dynamics (IV) Alex Wright video
10:45am Coffee Break SCGP Cafe
11:15am Birational geometry of moduli of curves (III) Gavril Farkas video
12:30pm Lunch SCGP Cafe
 2:00pm The geometry and topology of surface bundles (IV) Benson Farb video
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Problem session (until 6:00pm)  
 6:00pm Workshop banquet: Covered for all funded participants, funded locals, and speakers. SCGP Cafe  

Time Title Presenters  Video
 8:30am Breakfast begins (8:30am – 9:30am) SCGP Cafe
 9:30am Teichmüller dynamics (V) Alex Wright video
10:45am Coffee Break SCGP Cafe
11:15am Birational geometry of moduli of curves (IV) Gavril Farkas video
12:30pm Lunch SCGP Cafe
 2:00pm Birational geometry of moduli of curves (V) Gavril Farkas video
 3:30pm Tea Time SCGP Patio/Lobby

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