Colloquium

  • 2018 Nov 01

    Colloquium: Natan Rubin (BGU) - Crossing Lemmas, touching Jordan curves, and finding large cliques

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    It is a major challenge in Combinatorial Geometry to understand the intersection structure of the edges in a geometric or topological graph, in the Euclidean plane. One of the few "tight" results in this direction is the the Crossing Lemma (due to Ajtai, Chvatal, Newborn, and Szemeredi 1982, and independently Leighton 1983). It provides a relation between the number of edges in the graph and the number of crossings amongst these edges. This line of work led to several Ramsey-type questions of geometric nature.
  • 2018 Oct 25

    Colloquium: Karim Adiprasito (HUJI) - Combinatorics, topology and the standard conjectures beyond positivity

    2:30pm to 3:30pm

    Location: 

    Manchester Building (Hall 2), Hebrew University Jerusalem
    Consider a simplicial complex that allows for an embedding into R^d. How many faces of dimension d/2 or higher can it have? How dense can they be?
    This basic question goes back to Descartes. Using it and other rather fundamental combinatorial problems, I will motivate and introduce a version of Grothendieck's "standard conjectures" beyond positivity (which will be explored in detail in the Sunday Seminar).
    All notions used will be explained in the talk (I will make an effort to be very elementary)
  • 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.

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