Abstract: Let G be a Chevalley group scheme with elementary group E. Using a localization procedure to reduce to the well understood case of local rings, we study the following problems over a commutative ring R:
a) Normality of E(R) and commutator formulas;
b) Nilpotent structure of K1=G(R)/E(R)
c) bounded word length in E(R); and
d) normal subgroups of G(R).
Wednesday, April 24th
Freya Pritchard, CUNY
"Implicit systems of differential equations"
Time: 2:00 PM
Location: Hill 525
Abstract: We will consider implicit systems that are given by polynomial relations on the coordinates of the indeterminate function and the coordinates of the time derivative of the indeterminate function. For such implicit system of differential-algebraic equations, we will be concerned with algebraic constraints such that on the algebraic variety determined by the constraint equations the original implicit system of differential equations has an explicit representation.
Our approach to such systems is algebraic. Although there have been a number of articles that approach implicit differential equations algebraically, all such approaches have relied heavily on linear algebra. The approach that we will consider is different in that we have no linearity requirements at all, instead we shall rely on classical algebraic geometry. In particular we will use birational mappings to produce an explicit system of differential equations and an algebraic variety of possible initial values.
Wednesday, April 17th
Charlie Siegel, IPMU Japan
"Cyclic Covers, Prym Varieties and the Schottky-Jung Relations"
Time: 2:00 PM
Location: Hill 525
Wednesday, April 10th
Lev Borisov, Rutgers University
"Hilbert modular threefolds of discriminant 49"
Time: 2:00 PM
Location: Hill 525
Wednesday, April 3rd
Joe Ross, USC
"Intersection theory on singular varieties"
Time: 2:00 PM
Location: Hill 525
Wednesday, March 13th
Mina Teicher , Bar-Ilan
"The 3 main problems in the braid group"
Time: 2:00 PM
Location: Hill 525
Wednesday, February 27th
Robert Guralnick, USC and IAS
"Strongly Dense Subgroups of Algebraic Groups "
Time: 2:00 PM
Location: Hill 525
Abstract: Let G be a simple algebraic group. A free finitely generated subgroup H of G is called strongly dense in G if every nonabelian subgroup of H is Zariski dense in G. We will discuss joint work with Breuillard, Green and Tao which shows that strongly dense subgroups exist (over sufficiently large fields) and some recent improvements on this by Brueillard, Guralnick and Larsen. This has applications to finding Cayley graphs of finite simple groups of Lie type and some results on generation of finite simple groups of Lie type. Using these ideas, we can also improve on results of Borel and Deligne-Sullivan related to the Hausdorff-Banach-Tarski paradox.
Wednesday, February 20th
Tatiana Bandman, Bar-Ilan
"Dynamics and surjectivity of some word maps on SL(2,q)"
Time: 2:00 PM
Location: Hill 525
Abstract: I will speak about a geometric approach, based on the classical trace map, for investigating dynamics, surjectivity and equidistribution of word maps on groups PSL(2,q) and SL(2,q). It was also used for a characterization of finite solvable groups by two-variable identities.
Wednesday, February 13th
V. Retakh, Rutgers University
"A geometric approach to noncommutative Laurent phenomenon"
Time: 2:00 PM
Location: Hill 525
Abstract: A composition of birational maps given by Laurent polynomials need not be a Laurent polynomial. When it does, we talk about the Laurent phenomenon. A large variety of examples of the Laurent phenomena for commuting variables comes from the theory of cluster algebras. Much less is known in the noncommutative case. I will present a number of the noncommutative Laurent phenomenoma of a "geometric origin."
This is a joint work with A. Berenstein.
Wednesday, February 6th
Chuck Weibel, Rutgers University
"What is a Derivator?"
Time: 2:00 PM
Location: Hill 525
Abstract: As the name implies, this is an introductory talk. Derivators were introduced in 1983 by Grothendieck in a 600-page manuscript, and refined in his 2000-page manuscript in 1991. They are designed to enhance triangulated categories, and have recently been used in the study of non-commutative algebraic geometry.
Wednesday, January 30th
Special Algebra Seminar
David Anderson , University of Paris
"Operational K-theory "
Time: 2:00 PM
Location: Hill 525
Abstract: TBA
Thursday, January 24th
Special Algebra Seminar
Daniel Erman , Univeristy of Michigan
"Equations, syzygies, and vector bundles"
Time: 2:00 PM
Location: Hill 705
Abstract: For a system of polynomial equations, it has long been
known that the relations (or syzygies) among the polynomials provide
geometric information about the corresponding projective variety. I
will describe a collection of new ideas about how to study syzygies,
and how these lead to classification results and a duality between
syzygies and vector bundles.
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