
Combinatorics/Algebra Seminar
The seminar meets Mondays at 4.10pm in Carver 290.
If you or a guest wish to talk, please visit the Post Office.
February 20
Dani Szpruch (Howard University): On the Shahidi local coefficients matrix.
Abstract:
The LanglandsShahidi method is one of the two main approaches for defining and studying automorphic Lfunctions. The core of this method is a meromorphic invariant associated with representations of quasisplit reductive groups defined over local fields. This meromorphic invariant arises from a uniqueness result known as the uniqueness of the Whittaker model. Among its local applications, one finds irreducibility results and a formula for Plancherel measures. In the context of metaplectic groups, which are nonlinear covering groups, uniqueness of the Whittaker model no longer holds. Nevertheless, an analog of the invariant does exist. In the talk we will give a new and simple interpretation to this analog for coverings of padic SL(2). We will also give local applications. The talk should be accessible to nonexperts.

March 27

Stefanie Wang: to be announced.

March 13

Spring break: no seminar.

February 27, March 6

Tathagata Basak: to be announced.

February 20

Dani Szpruch (Howard University): On the Shahidi local coefficients matrix.
Abstract:
The LanglandsShahidi method is one of the two main approaches for defining and studying automorphic Lfunctions. The core of this method is a meromorphic invariant associated with representations of quasisplit reductive groups defined over local fields. This meromorphic invariant arises from a uniqueness result known as the uniqueness of the Whittaker model. Among its local applications, one finds irreducibility results and a formula for Plancherel measures. In the context of metaplectic groups, which are nonlinear covering groups, uniqueness of the Whittaker model no longer holds. Nevertheless, an analog of the invariant does exist. In the talk we will give a new and simple interpretation to this analog for coverings of padic SL(2). We will also give local applications. The talk should be accessible to nonexperts.

February 13

Jonathan Smith: Duality for lattices and quasilattices.
Abstract:
The talk will first review the lattice duality of Hartonas and Dunn, which represents a lattice as a Galois connection between its meet and join semilattices. Lattices appear naturally in data analysis as the structures of Hardegree's notion of a natural kind, or Wille's concepts. When extending these ideas to the analysis of complex data arising from systems with distinct levels (as in mathematical biology, for example), one is then led naturally to the idea of a quasilattice as an ordered system of lattices. The second part of the talk will review the duality theory for quasilattices recently developed in joint work with Anna Romanowska.

February 6

Jonathan Smith: Duality for semilattice Galois connections.
Abstract:
Semilattice Galois connections underlie a large class of optimization algorithms. This talk will present the duality for semilattice Galois connections that is due to Hartonas and Dunn. In their version, the dual objects were taken as polarities, i.e., relations between sets. However, although there are times when the relational language of polarities is appropriate, there are other times when an equivalent but more algebraic concept of a pairing is to be preferred. Polarities and pairings are fundamental to Hardegree's notion of a natural kind, or Wille's concepts, which have now become basic tools in the analysis of big data.

January 30

Cliff Bergman: Probabilities of finite algebras.
Abstract:
We present a simple probability measure on the space of finite
algebras of a fixed similarity type. We shall use this to describe a
striking result of V. L. Murskii, as well as some related results.

January 23

Jiali Li: Congruence npermutable varieties.
Abstract:
Many experts have been doing research on characterizations of congruence npermutable varieties in many different ways. In 1973 Hagemann and Mitschke, generalizing Maltsev conditions, provided a simple and nice characterization of congruence npermutable varieties. We offer our own approach to the characterization of congruence npermutable varieties, inspired by the Kearnes/Tschantz lemma.

January 16

King Holiday: no seminar.
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