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# Events for March 2, 2018 from General and Seminar calendars

## Brown Bag Lunch Series on Teaching

**Abstract:** The Center for Teaching Excellence (CTE) supports instructor professional development related to teaching. An overview of Center services available to individuals and groups will be provided. The session will include a reflective engagement activity on learning and teaching.

## Newton-Okounkov Bodies

**Abstract:** In this talk, we introduce the notion of SAGBI (or canonical) basis for a subalgebra. This will be employed to give toric degenerations of Grassmannians.

## Mathematical Physics and Harmonic Analysis Seminar

**Abstract:** We start by reviewing the notion of “quantum graph”, its eigenfunctions and the problem of counting the number of their zeros. The nodal surplus of the n-th eigenfunction is defined as the number of its zeros minus (n-1). When the graph is composed of two or more blocks separated by bridges, we propose a way to define a “local nodal surplus” of a given block. Since the eigenfunction index n has no local meaning, the local nodal surplus has to be defined in an indirect way via the nodal-magnetic theorem of Berkolaiko, Colin de Verdière and Weyand.

We will discuss the properties of the local nodal surplus and their consequences. In particular, its symmetry properties allow us to prove the long-standing conjecture that the nodal surplus distribution for graphs with β disjoint loops is binomial with parameters (β,1/2).

The talk is based on joint work with Lior Alon and Ram Band, arXiv:1709.10413 (accepted to CMP).

## Algebra and Combinatorics Seminar

**Abstract:** In this talk, I will talk about a geometric way to construct representations of noncompact semisimple Lie groups, though no prior knowledge is required. Kirillov's coadjoint orbit method suggests that (unitary) irreducible representations can be constructed as geometric quantization of coadjoint orbits of the group. Except for a lot of evidence, the quantization scheme meets strong resistance in the case of noncompact semisimple groups. I will give a new perspective on the problem using deformation quantization of symplectic varieties and their Lagrangian subvarieties. This is joint work in progress with Conan Leung.

## Geometry Seminar

**Abstract:** I will discuss the Koszul modules introduced by Papadima and Suciu and their relation to Resonance Varieties and Alexander type invariants of finitely generated groups. In special case related to representations S_g(C^2) of SL_2 we get nilpotent modules whose nilpotency degree is related to Green conjecture for canonical curves of genus g. The talk is based on forthcoming work joint with Aprodu, Farkas, Papadima and Raicu.

**Time:** 12:30PM - 1:30PM

**Location:** Blocker 220

**Speaker:** Jean Layne, Texas A&M

**Title:** *Center for Teaching Excellence Offerings for Instructors*

**Time:** 1:00PM - 2:30PM

**Location:** BLOC 624

**Speaker:** Emanuele Ventura, Texas A&M University

**Title:** *SAGBI bases and Grassmannians*

**Time:** 1:50PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Gregory Berkolaiko, TAMU

**Title:** *Nodal count distribution of graph eigenfunctions*

We will discuss the properties of the local nodal surplus and their consequences. In particular, its symmetry properties allow us to prove the long-standing conjecture that the nodal surplus distribution for graphs with β disjoint loops is binomial with parameters (β,1/2).

The talk is based on joint work with Lior Alon and Ram Band, arXiv:1709.10413 (accepted to CMP).

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Shilin Yu, Texas A&M University

**Title:** *Quantization and representation theory*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 628

**Speaker:** J. Weyman, U. Conn.

**Title:** *Resonance varieties*