Lie Group/Quantum Mathematics Seminar
Organizers Lisa Carbone, Yi-Zhi
Lepowsky and Siddhartha Sahi.
Time Friday, 12:00 to 1:00 pm.
Place Hill 705.
Starting from Spring, 2008, the
Lie Group Seminar and Quantum Mathematics Seminar
have merged together to a single seminar called the
Lie Group/Quantum Mathematics
Seminar. This seminar also has a page
Lie Groups Quantum Mathematics Seminar,
maintained by email@example.com.
For the Lie Group/Quantum Mathematics seminar in previous
semesters, see this
For talks in the Quantum Mathematics Seminar from Spring, 1998 to
Fall, 2007, see
For a few years before 2008, the Quantum Mathematics Seminar
shared the time and place with the Algebra Seminar.
For talks in both the Algebra and
Quantum Mathematics Seminars in these few semesters, see the page
the Previous Rutgers Algebra Seminars. For all the seminars and colloquia in the department, see
the Seminars and Colloquia page.
- Speaker Thomas Lam, University of Michigan
- Speaker Florencia Orosz Hunziker, Yale University
- Title Fusion rules for the Virasoro algebra of central charge 25
- Time/place 2/1/2019, Friday, 12:00 in Hill 705
- Abstract In 1990 Feigin and Fuchs established a correspondence between the Verma modules for the Virasoro algebras of dual central charges $c$ and $26- c$. In later work, the irreducible quotient module $L(c,0)$ was proved to be a vertex operator algebra called the Virsasoro VOA of central charge $c$. In this talk we will discuss an extension of the Feigin-Fuchs correspondence to the vertex algebra setting for the case $c=1$ and $c=25$. We will prove the the fusion rules for the non-Verma irreducible $L(25,0)$-modules coincide the fusion rules for the non-Verma irreducible $L(1,0)$-modules.
- Speaker Robert Laugwitz, Rutgers University
- Speaker Yi-Zhi Huang, Rutgers University
- Title A construction of twisted modules for
grading-restricted vertex (super)algebras
- Time/place 2/15/2019, Friday, 12:00 in Hill 705
- Abstract We give a general and direct
construction of (grading-restricted generalized) twisted
modules for a grading-restricted vertex (super)algebra V
associated to an automorphism g of V. Even in the case that g is of finite order, finding such a construction
has been a long-standing problem in the representation
theory of vertex operator algebra and orbifold conformal
Besides twisted vertex operators, one crucial ingredient in this construction is what we call
the "twist vertex operators" or "twist fields." Assuming that
a grading-restricted vector space W
equipped with a set twisted fields
and a set of twist fields satisfy a weak commutativity for twisted fields,
a generalized weak commutativity for one twisted field and one twist field and
a number of other properties that are relatively easy to verify, we define a twisted vertex
operator map for W and prove that W equipped with this twisted vertex operator map
is a (grading-restricted generalized) g-twisted V-module. As a
class of examples, we construct (grading-restricted
generlized) twisted moduels for vertex operator algebras associated to affine Lie algebras.
- Speaker Nicola Tarasca, Rutgers University
- Title Vertex algebras and moduli spaces of curves
- Time/place 2/22/2019, Friday, 12:00 in Hill 705
- Abstract This talk will focus on geometric realizations of vertex algebras. The Virasoro uniformization provides an incarnation of the Virasoro algebra in the tangent space of the Hodge line bundle on moduli of algebraic curves with marked points and local coordinates. This allows to assign to certain representations of the Virasoro algebra a sheaf on moduli of curves together with a projective connection.
After reviewing some facts on curves and their moduli spaces, I will discuss the sheaves on moduli of stable curves obtained from coinvariants of modules over conformal vertex algebras, and identify their logarithmic projective connection. This is joint work with Chiara Damiolini and Angela Gibney.
- Speaker Mark Skandera, Lehigh University
- Title Total nonnegativity and induced sign characters of the Hecke algebra
- Time/place 3/1/2019, Friday, 12:00 in Hill 705
- Abstract Gantmacher's study of totally nonnegative (TNN) matrices in
eventually found applications in many areas of mathematics.
Descending from his work are problems
concerning TNN polynomials, those polynomial functions of n^2
variables which take nonnegative
values on TNN matrices. Closely related to TNN polynomials are
functions in the Hecke algebra
trace space whose evaluations at certain Hecke algebra elements yield
polynomials in N[q]. In all
cases, it would be desirable to combinatorially interpret the
resulting nonnegative numbers.
In 2017, Kaliszewski, Lambright, and the presenter found the first
cancellation-free combinatorial formula
for the evaluation of all elements of a basis of V at all elements of
a basis of the Hecke algebra.
We will discuss a recent improvement upon this result which also
advances our understanding of TNN
polynomials. This is joint work with Adam Clearwater.
- Speaker Daniel Nakano, University of Georgia
- Time/place 3/29/2019, Friday, 12:00 in Hill 705
- Speaker Thomas Creutzig, University of Alberta
- Time/place 4/12/2019, Friday, 12:00 in Hill 705
- Speaker Juan Villarreal, Virginia Commonwealth
- Time/place 4/26/2019, Friday, 12:00 in Hill 705