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20 10, 2021

## Homological Mirror Symmetry for Hypersurface Singularities

2021-10-21T12:35:26+03:00October 20th, 2021|Joint ICMS & IMSA Seminar|

In this talk, I will briefly introduce homological mirror symmetry for certain hypersurface singularities. I will introduce basic definitions, Berglund-Hubsch duality of invertible polynomials, and some known results. Then I will discuss several examples in detail.

8 10, 2021

## More instances of Steenbrink Spectra in Singularity Categories

2021-10-16T13:48:03+03:00October 8th, 2021|Joint ICMS & IMSA Seminar|

Now that we have set up the Frobenius Manifold of a singularity, we can see 2 more places where the steenbrink spectrum of a singularity appears in its singularity category. Namely, the non-commutative mixed hodge structure of a singularity and the dimensional properties of the category. The former appearance being somehow natural, and the latter somewhat mysterious. In this talk we'll conduct a surface level investigation of these appearances.

8 10, 2021

## Windows and the BGMN conjecture

2021-10-26T14:31:25+03:00October 8th, 2021|Joint ICMS & IMSA Seminar|

Let $C$ be a smooth projective curve of genus at least 2, and let $N$ be the moduli space of semistable rank-two vector bundles of odd degree on $C$. We construct a semi-orthogonal decomposition in the derived category of $N$ conjectured by Belmans, Galkin and Mukhopadhyay and by Narasimhan. It has blocks of the form $D(C_d)$ where $C_d$ are $d$-th symmetric powers of $C$, and the semi-orthogonal complement to these blocks is conjecturally trivial. In order to prove our result, we use the moduli spaces of stable pairs over $C$. Such spaces are related to each other via GIT wall crossing, and the method of windows allows us to understand the relationship between the derived categories on either side of a given wall. This is a joint work with J. Tevelev.

20 08, 2021

## Joint Seminar – August 20, 2021

2021-10-16T13:19:32+03:00August 20th, 2021|Joint ICMS & IMSA Seminar|

On August 20, 2021, Prof. Rene Mboro gave the talk "On determinantal cubic hypersurfaces" and prof. Rodolfo Aguilar gave the talk "Quantum representations of fundamental groups of curves with infinite image."

27 07, 2021

## Spectra and Applications

2021-10-16T13:07:58+03:00July 27th, 2021|Joint ICMS & IMSA Seminar|

This is a survey course on the relation of the invariants of 3 manifolds and singularity theory. Using the theory of differential equations we relate classical 3 dimensional theory with modern category theory. Applications to Birational geometry and uniformization will be discussed.