# Abstracts for Mathematische Arbeitstagung 2015

Alternatively have a look at the program.

## The MNOP conjecture

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Speaker:
Richard Thomas
Date:
Fri, 2015-06-26 17:00 - 18:00
Location:
MPIM Lecture Hall

I will review the Maulik-Nekrasov-Okounkov-Pandharipande conjecture, relating two different ways of counting curves in an algebraic variety X of dimension 3 or less. The first counts holomorphic maps of curves into X, or parameterised curves, and gives Gromov-Witten theory. The second counts embedded curves in X cut out by equations, or unparameterised curves, and is called stable pair theory. The conjecture is that these theories contain the same information, but with a complicated, mysterious transformation between the two sets of invariants. I will describe an applica

## Volumes of moduli spaces in counting simple closed geodesics on flat surfaces, and in measuring diffusion in periodic billiards. Part 1

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Speaker:
Anton Zorich
Date:
Sat, 2015-06-27 09:30 - 10:30
Location:
MPIM Lecture Hall

## The topological recursion -- an inductive mechanism of counting on the moduli of curves. Part 1

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Speaker:
Motohico Mulase
Date:
Sat, 2015-06-27 11:00 - 12:00
Location:
MPIM Lecture Hall

In these lectures, the notion of the topological recursion is introduced through enumerative geometry problems, such as counting simple Hurwitz numbers and the number of lattice points on the moduli space of pointed curves.

## The uniformization of $\mathcal{A}_6$

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Speaker:
Gavril Farkas
Date:
Sat, 2015-06-27 14:30 - 15:30
Location:
MPIM Lecture Hall

## $S$-unit and Mordell equations via modularity

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Speaker:
Benjamin Matschke
Date:
Sat, 2015-06-27 16:00 - 17:00
Location:
MPIM Lecture Hall

## Cycles on the moduli space of curves. Part 1

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Speaker:
Rahul Pandharipande
Date:
Sun, 2015-06-28 09:30 - 10:30
Location:
MPIM Lecture Hall

I will give two lectures on the intersection theory of the moduli space of curves: tautological classes, relations, integral calculus, and cycle formulas. The role of the virtual fundamental class of the moduli of stable maps will be highlighted. In the second lecture, I will discuss the recent proof of Pixton's formula for double ramification cycles (joint work with Janda, Pixton, and Zvonkine).

## Tropical counting problems on moduli spaces

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Speaker:
Hannah Markwig
Date:
Sun, 2015-06-28 11:00 - 12:00
Location:
MPIM Lecture Hall

## Volumes of moduli spaces in counting simple closed geodesics on flat surfaces, and in measuring diffusion in periodic billiards. Part 2

Posted in
Speaker:
Anton Zorich
Date:
Sun, 2015-06-28 14:30 - 15:30
Location:
MPIM Lecture Hall

## Mirror symmetry out of Fano varieties

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Speaker:
Vasily Golyshev
Date:
Sun, 2015-06-28 16:00 - 17:00
Location:
MPIM Lecture Hall

## Cycles on the moduli space of curves. Part 2

Posted in
Speaker:
Rahu Pandharipande
Date:
Mon, 2015-06-29 09:30 - 10:30
Location:
MPIM Lecture Hall

I will give two lectures on the intersection theory of the moduli space of curves: tautological classes, relations, integral calculus, and cycle formulas. The role of the virtual fundamental class of the moduli of stable maps will be highlighted. In the second lecture, I will discuss the recent proof of Pixton's formula for double ramification cycles (joint work with Janda, Pixton, and Zvonkine).

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