From left: **Christopher Hacon, Claire Voisin, Ulrike Tillmann, François Labourie**

**Update:** This was a great event with four great inspiring talks.

# Abel in Jerusalem, January 12, 2020

### The *Einstein Institute of mathematics* is happy to host the **Abel in Jerusalem** Conference

**Abel in Jerusalem**

“* Abel in Jerusalem*” will be the 10th one-day conference with lectures aimed at a mathematically educated and interested audience, with the objective of increasing public awareness of mathematics and of the Abel Prize.

### Program

**9:40-10:00** Opening Remarks by **Hans Petter Graver**, President of the Norwegian Academy of Science and Letters

**10:00-11:00** **Christopher Hacon** (University of Utah): *Geometry of complex algebraic varieties* Abstract

11:00-11:30 Coffee Break

**11:30-12:30** **Ulrike Tillmann** (Oxford University): *Manifolds via cobordisms: old and new* Abstract

12:30-14:30 Lunch Break

**14:30-15:30** **Claire Voisin** (Collège de France): *Diagonals in algebraic geometry* Abstract

15:30-16:00 Coffee Break

**16:00-17:00** **François Labourie** (Université Côte d’Azur): *Counting curves and building surfaces: some works of Maryam Mirzakhani* Abstract

17:00-17:15 Closing remarks

17:15 – Transport to a reception at the King David Hotel

17:30 – Reception

19:00 – End of program

### Abstracts

### Christopher Hacon: Geometry of complex algebraic varieties

Abstract: Algebraic varieties are geometric objects defined by polynomial equations. The minimal model program (MMP) is an ambitous program that aims to classify algebraic varieties. According to the MMP, there are 3 building blocks: Fano varieties, Calabi-Yau varieties and varieties of general type which are higher dimensional analogs of Riemann surfaces of genus 0, 1, and greater or equal to 2. In this talk I will recall the general features of the MMP and discuss recent advances in our understanding of Fano varieties and varieties of general type.

### Ulrike Tillmann: Manifolds via cobordisms: old and new

Abstract: Manifolds are a fundamental mathematical structure of central importance to geometry. The notion of cobordism has played an important role in their classification since Thom’s work in the 1950s. In a different way, cobordisms are key to Atiyah’s axiomatic formulation of topological quantum field theory. We will explain how the two seemingly unrelated appearances of cobordisms have come together to give us a new approach to study the topology of manifolds and their diffeomorphisms. In addition to my own work, the talk will draw on results by Madsen, Weiss, Galatius and Randal-Williams.

### Claire Voisin: Diagonals in algebraic geometry

Abstract: The diagonal of a manifold appears naturally in topology, for example in the Hopf formula. Furthermore, the Künneth decomposition for the class of the diagonal controls the torsion in integral cohomology. In the context of algebraic geometry, I will discuss a weaker notion of decomposition of the diagonal, which has important applications in the study of rationality of algebraic varieties.

### François Labourie: Counting curves and building surfaces: some works of Maryam Mirzakhani

Abstract: I will use some works of Maryam Mirzakhani as a thread to explain very basic and elementary facts of geometry : how to build surfaces, how to count curves on surfaces, what is hyperbolic geometry. The talk will be elementary and most of it will be targeting undergraduate students.