Friday Evening:
Attendees arrive at the Anza-Borrego Research Station prior to 8pm
Saturday:
8am - Breakfast cooked by Group 1, clean-up by Group 2
10am - Talk 1: What is the Character Variety?
Speaker: Christina Grossack
Abstract: TBA
11:30 am - break
Noon - Talk 2: Intro to Higgs Bundles
Speaker: Charlie Wu
Abstract: We introduce the category of Higgs bundles on smooth proper curves over the complex numbers. Using non-abelian Hodge theory, we give easy proofs of topological properties of SL_2-character varieties for a genus two curve. Then, we discuss the cohomology of Higgs bundles and the geometry of the Dolbeault moduli space.
1:30 pm - Lunch
3pm - Talk 3: Abelian Kähler Hodge Theory
Speaker: Elliot Kienlze
Abstract: TBA
4:30 pm - Break
5pm - Dinner cooked by Group 3, clean-up by Group 4
Sunday:
8am - Breakfast cooked by Group 4, clean-up by Group 3
10am - Talk 4: Harmonicity
Speaker: David Weed
Abstract: TBA
11:30 am - Break
Noon - Talk 5: Corlette-Donaldson Theorem
Speaker: Nerea Alonso Garcia
Abstract: For a compact Riemann surface, the celebrated Non Abelian Hodge (NAH) correspondence provides a homeomorphism between the moduli space of Higgs bundles and the moduli space of holomorphic connections. The proof of the NAH contains two main steps: Corlette-Donaldson's Theorem and Hitchin-Simpson's Theorem. The goal of this talk is to sketch the proof of the first one. In order to that we will need to explore connections on vector bundles, equivariant maps and harmonic metrics.
1:30 pm - Lunch
3 pm - Talk 6: Hitchin-Simpson Correspondence
Speaker: Lam Nguyen
Abstract: In this talk, we state and sketch the proof of the theorem of Hitchin-Simpson. This theorem provides one direction of the non-abelian Hodge correspondence between the moduli space of polystable Higgs bundles and completely reducible representations of the fundamental group. Informally, it states that a Higgs bundle is polystable if and only if it harmonic. We will recall the necessary definitions and sketch out the key analytic steps in the proof following the notes of Richard Wentworth.
4:30 pm - Break
5pm - Dinner cooked by Group 2, clean-up by Group 1