# Algebra & Combinatorics Seminar:   2019–20

The Algebra & Combinatorics Seminar meets (usually) on Fridays from 3–4 pm, in Lecture Hall LH-1 of the IISc Mathematics Department. The organizers are Apoorva Khare and R. Venkatesh.

### Autumn 2019

 Terrence George (Brown University, USA) Aug 7, 2019 Dimers and the Beauville integrable system (note: unusual day)

Abstract. To any convex integral polygon $N$ is associated a cluster integrable system that arises from the dimer model on certain bipartite graphs on a torus. The large scale statistical mechanical properties of the dimer model are largely determined by an algebraic curve, the spectral curve $C$ of its Kasteleyn operator $K(x,y)$. The vanishing locus of the determinant of $K(x,y)$ defines the curve $C$ and coker $K(x,y)$ defines a line bundle on $C$. We show that this spectral data provides a birational isomorphism of the dimer integrable system with the Beauville integrable system related to the toric surface constructed from $N$.

This is joint work with Alexander Goncharov and Richard Kenyon.

 Nikhil Srivastava (University of California, Berkeley, USA) Aug 16, 2019 Quantitative Diagonalizability (speaking in the Eigenfunctions Seminar)

 Apoorva Khare (IISc Mathematics) Aug 23, 2019 Density: How Zariski helped Schur, Cayley, and Hamilton

Abstract. Computing the determinant using the Schur complement of an invertible minor is well-known to undergraduates. Perhaps less well-known is why this works even when the minor is not invertible. Using this and the Cayley–Hamilton theorem as illustrative examples, I will gently explain one "practical" usefulness of Zariski density outside commutative algebra.

 Soumik Pal (University of Washington, Seattle, USA) Aug 30, 2019 Entropic relaxations of Monge–Kantorovich optimal transports (speaking in the Eigenfunctions Seminar; no Alg–Comb today)

 Guhan Venkat (Université Laval, Quebec, Canada; and Morningside Center of Mathematics, Beijing, China) Sep 4, 2019 Stark–Heegner cycles for Bianchi modular forms

Abstract. In his seminal paper in 2001, Henri Darmon proposed a systematic construction of p-adic points, viz. Stark–Heegner points, on elliptic curves over the rational numbers. In this talk, I will report on the construction of p-adic cohomology classes/cycles in the Harris–Soudry–Taylor representation associated to a Bianchi cusp form, building on the ideas of Henri Darmon and Rotger–Seveso. These local cohomology classes are conjectured to be the restriction of global cohomology classes in an appropriate Bloch–Kato Selmer group and have consequences towards the Bloch–Kato–Beilinson conjecture as well as Gross–Zagier type results. This is based on a joint work with Chris Williams (Imperial College London).

 Chandan Dalawat (Harish-Chandra Research Institute, Allahabad) Sep 6, 2019 TBA

Abstract. TBA

 Prasad Tetali (Georgia Tech, Atlanta, USA) Sep 13, 2019 TBA

Abstract. TBA

 Rekha Biswal (Max Planck Institut, Bonn, Germany) Sep 16, 2019 TBA (note: unusual day)

Abstract. TBA

 Rajeeva Karandikar (CMI, Chennai) Sep 27, 2019 TBA (speaking in the Eigenfunctions Seminar; no Alg–Comb today)

 Bikramaditya Sahu (IISc Mathematics) Oct 04, 2019 TBA

Abstract. TBA

 Atul Dixit (IIT, Gandhinagar) Oct 9, 2019 TBA (note: unusual day)

Abstract. TBA

 Atul Dixit (IIT, Gandhinagar) Oct 11, 2019 TBA (speaking in the Eigenfunctions Seminar)

 Uri Onn (Australian National University, Canberra, Australia) Oct 25, 2019 TBA

Abstract. TBA

 L. Sunil Chandran (IISc CSA) Nov 8, 2019 TBA

Abstract. TBA

 John Meakin (University of Nebraska at Lincoln, USA) Dec 3, 2019 TBA (note: unusual day)

Abstract. TBA

2018–19