**Joint ICMS & IMSA Seminar**

August Hozie*University of Miami & IMSA*

**Some Examples and Asymptotics of Irregular Connections of Singularities**

Friday, December 10, 2021, 9:30am

Hybrid

**Abstract:** A common feature of Noncommutative Hodge Structures, Frobenius Manifolds, and Irregular Hodge Structures is a connection on P1 which is Poincare rank 1 irregular at 0 and regular at infinity. In many cases we can compute local equations for these connections and investigate their asymptotics at the singular point. In this talk we'll look at some examples of the asymptotic spectra associated with these equations and some behavior under deformation.

**Joint ICMS & IMSA Seminar**

Dr. Ludmil Katzarkov*University of Miami*

**Multispectra**

Monday, November 22, 2021, 5:00pm

Hybrid*Click here to view video*

**Abstract:** We will describe some new birational invariants.

**Joint ICMS & IMSA Seminar**

Dr. Shaoyun Bai*Princeton University*

**On the Rouquier Dimension of Wrapped Fukaya Categories**

Monday, November 22, 2021, 4:00pm

Hybrid*Click here to view video*

**Abstract:** Given a triangulated category, its Rouquier dimension is defined to be the minimal generation time of all of its split-generators. I will explain how the Rouquier dimension of derived wrapped Fukaya categories of Weinstein manifolds/sectors is related to problems in symlectic topology of classical flavor, including quantitative intersection question of Lagrangian skeleta and estimating minimal numbers of critical points of symplectic Lefschetz fibrations. Moreover, using recent advances on symplectic flexibility (the arboreal program) and the local-to-global characterization of wrapped Fukaya categories, I will show how to resolve new cases of Orlov’s conjecture by bounding the Rouquier dimension of derived categories of algebraic varieties using homological mirror symmetry. This is joint work with Laurent Cote.

**Joint ICMS & IMSA Seminar**

Dr. Kyoung-Seog Lee*University of Miami & IMSA*

**Homological Mirror Symmetry for Hypersurface Singularities II**

Friday, November 5, 2021, 9:30am

Hybrid*Click here to view video*

**Abstract:** In this talk, I will continue to introduce homological mirror symmetry for singularities. I will explain the categories of graded matrix factorizations of invertible polynomials and discuss several ways to describe them. If time permits, I will discuss stability conditions on the categories of the graded matrix factorizations of weighted homogeneous polynomials constructed by Takahashi, Kajiura-Saito-Takahashi, Toda, Otani-Takahashi.

**Joint ICMS & IMSA Seminar**

Dr. Kyoung-Seog Lee*University of Miami & IMSA*

**Homological Mirror Symmetry for Hypersurface Singularities I**

Friday, October 22, 2021, 9:30am

Hybrid*Click here to view video*

**Abstract:** 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.

**IMSA Seminar**

Dr. Han-Bom Moon*Fordham & Stanford*

**Conformal Blocks in Algebraic Geometry Part III**

Thursday, October 14, 2021, 2:15pm

Hybrid

**Abstract:** In this series of lectures, I briefly introduce mathematical aspects of the WZW model and the theory of conformal blocks. I will discuss the formal definition and basic properties of conformal blocks and how they are related to the geometric study of moduli spaces of curves and parabolic bundles. Most of the lectures will be accessible for non-experts and graduate students.

**IMSA Seminar**

Dr. Han-Bom Moon*Fordham & Stanford*

**Conformal Blocks in Algebraic Geometry Part II**

Thursday, October 14, 2021, 1:00pm

Hybrid

**Abstract:** In this series of lectures, I briefly introduce mathematical aspects of the WZW model and the theory of conformal blocks. I will discuss the formal definition and basic properties of conformal blocks and how they are related to the geometric study of moduli spaces of curves and parabolic bundles. Most of the lectures will be accessible for non-experts and graduate students.

**IMSA Seminar**

Dr. Han-Bom Moon*Fordham & Stanford*

**Conformal Blocks in Algebraic Geometry Part I**

Wednesday, October 13, 2021, 2:00pm

Hybrid

**Abstract:** In this series of lectures, I briefly introduce mathematical aspects of the WZW model and the theory of conformal blocks. I will discuss the formal definition and basic properties of conformal blocks and how they are related to the geometric study of moduli spaces of curves and parabolic bundles. Most of the lectures will be accessible for non-experts and graduate students.

**Joint ICMS & IMSA Seminar**

August Hozie*University of Miami & IMSA*

**More Instances of Steenbrink Spectra in Singularity Categories**

Friday, October 8, 2021, 9:50am

Hybrid*Click here to view video*

**Abstract:** 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 is somehow natural, and the latter somewhat mysterious. In this talk we will conduct a surface level investigation of these appearances.

**Joint ICMS & IMSA Seminar**

Sebastian Torres*ICMS-Sofia*

**Windows and the BGMN Conjecture**

Friday, October 8, 2021, 8:30am

Via Zoom*Click here to view video*

**Abstract: **Let

In order to prove our result, we use the moduli spaces of stable pairs over

This is a joint work with J. Tevelev.

This event is organized by the International Center for Mathematical Sciences – Sofia (ICMS-Sofia). To view more information regarding this seminar, click here.

**Joint ICMS & IMSA Seminar**

August Hozie*University of Miami & IMSA*

**Steenbrink Spectra in Singularity Categories**

Friday, October 1, 2021, 9:30am

Hybrid*Click here to view video*

**Abstract:** The spectrum of a singularity as defined by Steenbrink encodes important analytic information about a singularity and describes the Hodge filtration on the vanishing cycles of the singularity. In this talk we will explore a few different ways in which the spectral numbers show up in the triangulated singularity category associated with a singularity.

**Joint ICMS & IMSA Seminar**

Dr. Kyoung-Seog Lee*University of Miami & IMSA*

**Alexander Polynomials of Algebraic Links**

Friday, September 24, 2021, 9:30am

Hybrid*Click here to view video*

**Abstract:** The Alexander polynomial is one of the most well-known invariants in knot theory. In the first part of this talk, I will review basic definitions and examples of Alexander polynomials of algebraic links. Then I will survey several results expressing Alexander polynomials of algebraic links via tools of algebraic geometry. Then I will discuss briefly how the spectrum of a plane curve singularity is related to the Alexander polynomial of its algebraic link.

**Joint ICMS & IMSA Seminar**

Dr. Kyoung-Seog Lee*University of Miami & IMSA*

**Plane Curve Singularities and Spectrum **

Friday, September 17, 2021, 9:30am

Hybrid

**Abstract:** In the first part of this talk, I will review basic notions and results about plane curve singularities, e.g. blow-ups, resolution of singularities, Newton-Puiseux series, etc. Then I will explain how to compute the spectrum of a plane curve singularity via Newton-Puiseux series based on Morihiko Saito's work.

**IMSA Seminar**

Josef Svoboda*University of Miami & IMSA*

**Surface Singularities and Invariants of their Links**

Friday, September 10, 2021, 9:30am

Hybrid*Click here to view video*

**Abstract:** To an isolated surface singularity, we can assign a natural 3-manifold - the link of the singularity. It is an old question how many of the properties of the singularity can be recovered from this purely topological information. Based on the work of Lawrence-Zagier, Hikami and others, I will show how quantum topological invariants of the link are related to the spectrum in the case of Brieskorn spheres.

**IMSA Seminar**

Josef Svoboda*University of Miami & IMSA*

**Spectrum of Singularities**

Friday, September 3, 2021, 9:30am

Hybrid*Click here to view video*

**Abstract:** The spectrum is a strong invariant of a hypersurface singularity, defined originally by Arnold, Varchenko and Steenbrink. I will start with examples of singularities and their spectra and sketch the definition of the spectrum. Then I will concentrate on the most important properties of the spectrum such as the Thom-Sebastiani theorem and semicontinuity, which are very powerful in applications. Finally, I will talk about computational techniques to obtain the spectrum.

**Joint ICMS & IMSA Seminar**

Dr. Rodolfo Aguilar*ICMS*

**Quantum Representations of Fundamental Groups of Curves with Infinite Image**

Friday, August 20, 2021, 10:30am (5:30pm Sofia)

Online*Click here to view video*

**Abstract:** We will report some results due to Koberda-Santharoubane showing an element of $\pi_1(\mathbb{P}^1\setminus \{3-\text{points}\})$ having infinite order under some quantum representations of the mapping class group.

This event is organized by the International Center for Mathematical Sciences – Sofia (ICMS-Sofia). To view more information regarding this seminar, click here.

**Joint ICMS & IMSA Seminar**

Dr. Rene Mboro*ICMS*

**On Determinantal Cubic Hypersurfaces (after Iliev-Manivel, Beauville,...)**

Friday, August 20, 2021, 9:30am (4:30pm Sofia)

Online*Click here to view video*

**Abstract:** We give an account of the problem of writting an equation of a cubic (or other degree) hypersurface $X$ as a (kind of) determinant of a matrix with homogeneous entries. Expressing the equation of $X$ as a determinant is equivalent to produce a arithmetically Cohen-Macaulay vector bundle on $X$. The talk will focus on the cases of cubic hypersurfaces of dimension at most 8.

This event is organized by the International Center for Mathematical Sciences – Sofia (ICMS-Sofia). To view more information regarding this seminar, click here.