Basic notions seminar

Coordinates: DRL 4E19 on Thursdays at 12:30pm-1:30pm

Objective: 

This is a seminar for graduate students at UPenn where we focus on learning various basic objects in and around the following fields.

• Riemann-Hilbert correspondence

[Oct 16, Emerson] NAH - moduli perspective

References: 

1. Porta and Sala, Simpson’s shapes of schemes and stacks.

2. Simpson, Nonabelian Hodge Theory.

3. Simpson, Algebraic aspects of higher nonabelian Hodge theory.

• Derived geometry

[Oct 23, Avik] Cotangent complex

[Oct 30, Ana] Shifted symplectic structure

[Nov 6, Ana] Shifted Poisson structure

References: 

4. Pantev and Vezzosi, Introductory topics in derived algebraic geometry.

5. Pantev, Toen, Vaquie and Vezzosi, Shifted symplectic structures.

6. Calaque, Pantev, Toen, Vaquie and Vezzosi, Shifted Poisson structures and deformation quantization.

• nc Hodge structures and Hodge atoms

[Nov 13, Victor] Frobenius manifolds and Gromov-Witten theory

[Nov 21, Emerson] Non-commutative Hodge structures

[Nov 28, Emmett] Maximal and over-maximal F-bundles

[Dec 03, Avik] A-model F-bundles

[Dec 10, Ana] G-atoms and Hodge atoms

References: 

7. Lee-Pandaripande - Gromov-Witten theory

8. Kontsevich, Katzarkov and Pantev - Hodge theoratic aspects of Mirror symmetry

9. Kontsevich,Katzarkov, Pantev and Yu - BIRATIONAL INVARIANTS FROM HODGE STRUCTURES AND QUANTUM MULTIPLICATION

Some references:

Shifted symplectic/Poisson structures: PTVV, CPTVV, Cal18, Saf17, TV18, Kal08, PV18

nc Hodge structures: KKP, KKPY, Kon05, Sab11, Sab16

nc Hodge and Mirror: KKP, Har21, Sah18

LG-models: Har21, Sah18, KP, AKO1, AKO2, Aur07

DQ: Kont02, Gutt, PTVV, CPTVV, Toen

RH:  KS24

Hitchin: dCHM12, Mauri, Hausel, Maulik, CDP12