Amitsur Algebra

  • 2018 Jun 26

    Amitsur Symposium: Lev Glebsky - "Approximations of groups by finite and linear groups"

    4:30pm to 5:30pm

    Location: 

    Manchester House, Lecture Hall 2
    The sofic groups and hyperlinear groups are groups approximable by finite symmetric
    and by unitary groups, respectively. I recall their definitions and discuss why those classes of groups are interesting. Then I consider approximations by other classes of groups and review some results, including rather recent ones by N. Nikolov, J. Schneider, A.Thom, https://arxiv.org/abs/1703.06092 .
    If time permits I'll speak about stability and its relations with approximability.
  • 2018 Jun 26

    Amitsur Symposium: Aner Shalev - "The length and depth of finite groups, algebraic groups and Lie groups"

    3:00pm to 4:00pm

    Location: 

    Manchester House, Lecture Hall 2
    The length of a finite group G is defined to be the maximal length of an unrefinable chain of subgroups going from G to 1. This notion was studied by many authors since the 1940s.
    Recently there is growing interest also in the depth of G, which is the minimal length of such a chain. Moreover, similar notions were defined and studied for important families of infinite groups, such as connected algebraic groups and connected Lie groups.
  • 2018 Jun 26

    Amitsur Symposium: Arye Juhasz - "On the center of Artin groups"

    2:00pm to 3:00pm

    Location: 

    Manchester House, Lecture Hall 2
    Let A be an Artin group. It is known that if A is spherical (of finite type) and irreducible (not a direct sum), then it has infinite cyclic center.
    It is conjectured that all other irreducible Artin groups have trivial center. I prove this conjecture under a stronger assumption that not being spherical namely, if there is a standard generator which is not contained in any 3-generated spherical standard parabolic subgroup. The main tool is relative presentations of Artin groups.
  • 2018 Jun 26

    Amitsur Symposium: Malka Schaps - "Symmetric Kashivara crystals of type A in low rank"

    11:30am to 12:30pm

    Location: 

    Manchester House, Lecture Hall 2
    The basis of elements of the highest weight representations of affine Lie algebra of type A can be labeled in three different ways, my multipartitions, by piecewise linear paths in the weight space, and by canonical basis elements. The entire infinite basis is recursively generated from the highest weight vector of operators f_i from the Chevalley basis of the affine Lie algebra, and organized into a crystal called a Kashiwara crystal. We describe cases where one can move between the different labelings in a non-recursive fashion, particularly when the crystal has some symmetry.
  • 2018 Jun 26

    Amitsur Symposium: Alex Lubotzky - "First order rigidity of high-rank arithmetic groups"

    10:00am to 11:00am

    Location: 

    Manchester House, Lecture Hall 2
    The family of high rank arithmetic groups is a class of groups playing an important role in various areas of mathematics.
    It includes SL(n,Z), for n>2 , SL(n, Z[1/p] ) for n>1, their finite index subgroups and many more.
    A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity.
  • 2017 Dec 28

    Amitsur Algebra: Ari Shnidman (Boston College), "The behavior of rational points in one-parameter families"

    12:00pm to 1:00pm

    Location: 

    Ross 70, Math Building, Givat Ram

    Title: The behavior of rational points in one-parameter families
    Abstract: How often does a "random" algebraic plane curve f(x,y) = 0
    have a solution with rational coordinates? In one-parameter "twist"
    families of elliptic curves, Goldfeld conjectured that there should be
    a rational point exactly half of the time. Recent progress towards
    this conjecture makes use of Selmer groups, and I'll explain the
    geometric idea underlying their construction. I'll also describe
    results for families of curves of higher genus, and abelian varieties
  • 2017 Jun 29

    Amitsur Algebra: Nir Gadish

    12:00pm to 1:00pm

    Location: 

    Manchester 209
    Title: Stability patterns in representation theory and applications
    Abstract:
    Many natural sequences of objects come equipped with group actions, e.g. the symmetric group on n letters acting on a space X_n. This leads to fundamental instability of invariants, such as homology, arising from the representation theory of the sequence of groups. Representation stability is a new and increasingly important set of ideas that describe a sense in which such sequence of representations (of different groups) stabilizes.
  • 2017 Jun 22

    Amitsur Algebra: Jan Dobrowolski

    12:00pm to 1:00pm

    Location: 

    Manchester 209
    Title: Inp-minimal ordered groups.
    Abstract. The main goal of the talk is to present the proof of the theorem stating that inp-minimal (left)-ordered groups are abelian. This generalizes a previous result of P. Simon for bi-ordered inp-minimal groups.
  • 2017 May 25

    Amitsur Algebra: Katrin Tent, "Sharply 2- and 3-transitive groups"

    12:00pm to 1:00pm

    Location: 

    Manchester 209
    The existence of sharply 2-transitive groups without regular normal subgroup was a longstanding open problem. Recently constructions have been given, at least in certain characteristics. We will survey the current state of the art and explain some constructions and their limitations. (joint work with E. Rips)

Pages