• 2018 Oct 18

# Colloquium: Rahul Pandharipande (ETH Zürich) - Zabrodsky Lecture: Geometry of the moduli space of curves

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions in the study of tautological classes on the moduli space following ideas and conjectures of Mumford, Faber-Zagier, and Pixton. Cohomological Field Theories (CohFTs) play an important role. The talk is about the search for a cohomology calculus for the moduli space of curves parallel to what is known for better understood geometries.
• 2018 Oct 18

# Zabrodsky Lecture 1: Geometry of the moduli space of curves

## Lecturer:

Rahul Pandharipande (ETH Zurich)
2:30pm to 3:30pm

## Location:

Manchester House, Lecture Hall 2

The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions in the study of tautological classes on the moduli space following ideas and conjectures of Mumford, Faber-Zagier, and Pixton. Cohomological Field Theories (CohFTs) play an important role. The talk is about the search for a cohomology calculus for the moduli space of curves parallel to what is known for better understood geometries. My goal is to give a presentation of the progress in the past decade and the current state of the field.

• 2018 Jun 28

# Colloquium: Barry Simon (Caltech) - "More Tales of our Forefathers"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse. Among the mathematicians with vignettes are Riemann, Newton, Poincare, von Neumann, Kato, Loewner, Krein and Noether. This talk is in two parts. The second part will be given from 4:00 to 5:00 (not 5:30) in the Basic Notions seminar.
• 2018 Jun 21

# Colloquium: Erdos lecture - Canceled

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Given a convex polytope P, what is the number of integer points in P? This problem is of great interest in combinatorics and discrete geometry, with many important applications ranging from integer programming to statistics. From a computational point of view it is hopeless in any dimensions, as the knapsack problem is a special case. Perhaps surprisingly, in bounded dimension the problem becomes tractable. How far can one go? Can one count points in projections of P, finite intersections of such projections, etc.?
• 2018 Jun 14

# Colloquium - Zuchovitzky lecture: Lior Yanovski (HUJI) "Homotopy cardinality and the l-adic analyticity of Morava-Euler characteristic"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
A finite set has an interesting numerical invariant - its cardinality. There are two natural generalizations of "cardinality" to a (homotopy) invariant for (suitably finite) spaces. One is the classical Euler characteristic. The other is the Baez-Dolan "homotopy cardinality". These two invariants, both natural from a certain perspective, seem to be very different from each other yet mysteriously connected. The question of the precise relation between them was popularized by John Baez as one of the "mysteries of counting".
• 2018 Jun 07

# Colloquium: Gabriel Conant (Notre Dame) - "Pseudofinite groups, VC-dimension, and arithmetic regularity"

2:15pm to 3:15pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Given a set X, the notion of VC-dimension provides a way to measure randomness in collections of subsets of X. Specifically, the VC-dimension of a collection S of subsets of X is the largest integer d (if it exists) such that some d-element subset Y of X is ""shattered"" by S, meaning that every subset of Y can be obtained as the intersection of Y with some element of S. In this talk, we will focus on the case that X is a group G, and S is the collection of left translates of some fixed subset A of G.
• 2018 May 31

# Tamar Ziegler (Hebrew University) - "Concatenating cubic structure and polynomial patterns in primes"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
A major difficulty in finding polynomial patterns in primes is the need to understand their distribution properties at short scales. We describe how for some polynomial configurations one can overcome this problem by concatenating short scale behavior in "many directions" to long scale behavior for which tools from additive combinatorics are available.
• 2018 May 23

# Colloquium: Janos Pach (EPFL Lausanne, IIAS and Renyi Institute Budapest) - "The Crossing Lemma"

4:15pm to 5:15pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The Crossing Lemma of Ajtai, Chvátal, Newborn, Szemerédi (1982) and Leighton (1983 )states that if a graph of n vertices and e>4n edges is drawn in the plane, then the number of crossings between its edges must be at least constant times e^3/n^2. This statement, which is asymptotically tight, has found many applications in combinatorial geometry and in additive combinatorics. However, most results that were obtained using the Crossing Lemma do not appear to be optimal, and there is a quest for improved versions of the lemma for graphs satisfying certain special properties.
• 2018 May 17

# Colloquium - Tzafriri lecture: Amitay Kamber (Hebrew university) "Almost-Diameter of Quotient Spaces and Density Theorems"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
A recent result of Lubetzky and Peres showed that the random walk on a $q+1$-regular Ramanujan graph has $L^{1}$-cutoff, and that its “almost-diameter” is optimal. Similar optimal results were proven by other authors in various contexts, e.g. Parzanchevski-Sarnak for Golden Gates and Ghosh-Gorodnik-Nevo for Diophantine approximations. Those results rely in general on a naive Ramanujan conjecture, which is either very hard, unknown, or even false in some situations. We show that a general version of those results can be proven using the density hypothesis of Sarnak-Xue.
• 2018 May 10

# Colloquium: Zemer Kosloff (Hebrew University) - "Poisson point processes, suspensions and local diffeomprhisms of the real line"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The study of the representations theoretic properties of the group of diffeormorphisms of locally compact non compact Riemmanian manifolds which equal to the identity outside a compact set is is linked to a natural quasi invariant action of the group which moves all points of a Poisson point process according to the diffeomorphism (Gelfand-Graev-Vershik and Goldin et al.).
Neretin noticed that the local diffeomorphism group is a subgroup of a larger group which he called GMS and that GMS also acts in a similar manner on the Poisson point process.