All problems should be submitted via zoom/skype/etc. You need to have your solutions written down beforehand, then take photos of them (also beforehand), and use the share screen functionality to show your written solutions during a zoom/skype/etc session, explaining them while showing them on screen.

N.B. It is not enough to just send the written solutions! You need to explain all your solutions via zoom/skype/etc. Still, you need to have everything written down and copied (via taking a photo or scanning etc) to your device in order to be able to show the written solution alongside your explanation during the zoom/skype/etc session.

All problems should be submitted (according to the above rules) to teaching assistant Danil Gubarevitch. Please contact him via his email: danilphys180916 [at] mail.ru.

18.01

Introduction. (Notes; video).

22.01

Definitions of Frobenius algebras. (Video)

25.01

Examples of Frobenius algebras. +Talk by Alexei Piskunov, "Matrix algebras as Frobenius algebras". (Notes; video)

29.01

Relation between different Frobenius algebras built upon the same algebra. Symmetric Frobenius algebras. Potentials of Frobenius algebras. (Video)

01.02

Frobenius algebra of a hypersurface singularity --- Jacobian algebra. Product and pairing. +Talk by Anton Rarovskiy, "Residue pairing for Fermat type singularities". (Notes; Video)

05.02

Examples of potentials of Frobenius algebras, semisimplicity. (Video)

08.02

Talk by Feodor Selyanin, "Mirror symmetry for P^n". (Video)

12.02

Cobordisms. The definition of a TQFT. (Video)

15.02

Linear transformations of Frobenius algebras. Quasi-homogeneity of Frobenius algebra potentials. (Video)

19.02

Relation between 2d TQFTs and symmetric Frobenius algebras. +Talk by Ivan Motorin. (Video)

22.02

Examples and details of the relation between 2d TQFTs and Frobenius algebras. (Video)

26.02

TQFT correlators in higher genus. (Video)

01.03

Generators and relations for 2d cobordisms. (Notes, video)

05.03

Relation between 2d TQFTs and symmetric Frobenius algebras via generators and relations for 2d cobordisms. (Video)

12.03

Relations for TQFT correlators. (Video)

15.03

Moduli spaces of algebraic curves. (Video)

19.03

Stable curves and Deligne-Mumford compactification of moduli spaces of algebraic curves. (Video)

22.03

Structure and examples of Deligne-Mumford compactifications. (Video)

26.03

Boundary strata of moduli spaces of stable curves; smooth structure on the space of stable curves of genus zero. (Video)

05.04

Mirror pair of elliptic singularities. (Video)

09.04

Cohomology of compactified moduli spaces of genus zero. (Video)

12.04

Psi-classes and their integrals. (Video)

16.04

Definition of orbifolds. (Video)

19.04

Talk by Denis Lyskov + further computations in the cohomology of M_{0,n}, gluing morphism. (Video)

23.04

Orbifolds contd. (Video)

26.04

Talk by Keke Zhang, Cohomological field theories in genus 0. (Video)

30.04

WDVV equation, associativity condition. (Video)

14.05

Orbifolds as groupoids. (Video)

17.05

Talk by Anton Shlyapugin + GW theory of P1. (Video)

21.05

Chen-Ruan cohomology of global quotients. (Video)

24.05

Talk by Alex Krüger + an example of mirror symmetry. (Video)

Past talks:

25.01 -- A.Piskunov -- Frobenius structures on algebras of matrices

01.02 -- A.Rarovsky -- Residue pairing for Fermat type singularities

08.02 -- F.Selyanin -- Mirror symmetry for P^n

19.02 -- I.Motorin - Gluing technique for 2D cobordisms --- Lemma 2.3.13 from Kock's book should be presented with both proofs

19.04 -- D.Lyskov -- "Orbifolds "projective line with three points of orders (3,3,3) or (4,4,2) or (6,3,2)" can be obtained via the quotients of elliptic curves (or tori) by a finite group action"

26.04 -- K.Zhang -- "Examples of orbifold projective lines"

17.05 -- A.Shlyapugin -- "In the moduli space of the genus 0 curves the integral of any product of psi-classes is given by a multinomial coefficients"

Planned talks:

Alex Krueger --- "counting curves in P^2" --- prove the formula for the number of curves passing through 3d-1 points in general position via GW-theory of P^2. Reference is this Text. To be done is theorem on page. 2. Everything before it should be assumed as being given beforehand.