Alternatively have a look at the program.

## From topological recursion to integrable systems

Topological recursion associates to a spectral curve, a sequence of differential forms, and provides a candidate to be a Tau-function and Baker--Akhiezer function of an integrable system. The Baker--Akhiezer function would then obey an ODE, which can be called a "quantization" of the spectral curve. We will review some aspects of these topics.

## On singularities of spectral curves and SCFTs of class S

## BCFG Hitchin integrable systems via orbifoldings

An intriguing relationship between Hitchin integrable systems and Calabi--Yau integrable systems, both associated to any complex ADE Lie group of adjoint type, was discovered by Diaconescu, Donagi and Pantev in 2006. For each such ADE Lie group, the construction centers around a family of corresponding quasi-projective Calabi--Yau threefolds. In his 2016 thesis, Beck generalized this construction to include the non-simply laced complex simple Lie groups, whose Dynkin diagrams are obtained from some of the ADE Dynkin diagrams by "folding''.

## Genus zero open-closed mirror symmetry for toric Calabi–Yau $3$-orbifolds

We study genus zero open-closed orbifold Gromov–Witten invariants counting holomorphic disks in a symplectic toric Calabi–Yau 3-orbifolds with boundary in Lagrangians of Aganagic–Vafa type. I will describe an open mirror theorem which expresses generating functions of orbifold disk invariants in terms of Abel–Jacobi maps of the mirror curve, based on joint work with Bohan Fang and Hsian-Hua Tseng. This generalizes the open mirror theorem for symplectic toric Calabi–Yau 3-manifolds conjectured by Aganagic–Vafa, Aganagic–Klemm–Vafa and proved in joint work with Fang.

## Gamma conjecture via tropical geometry

In the context of mirror symmetry, people have observed that asymptotics of periods near the large complex structure limit involves characteristic numbers of mirror manifolds and Riemann zeta values. This phenomenon can be formulated in terms of the Gamma class.

In this talk, I will explain how zeta values appear from tropical geometry and SYZ picture. This is based on joint work with Mohammed Abouzaid, Sheel Ganatra and Nick Sheridan.

## Motivic Donaldson–Thomas invariants of the moduli stacks of parabolic Higgs bundles and bundles with connections

Using the ideas of motivic integration I will explain how to compute the "number" of semistable Higgs bundles (maybe with parabolic structure) of fixed rank and degree on a smooth complex curve. Based on that result I am going to discuss a similar problem in the case of bundles with connections. If time permits, I will explain open questions, including a conjectural relation to Satake correspondence for affine Grassmannians over 2-dimensional local rings. This is a joint project with Roman Fedorov and Alexander Soibelman.

## H3 surfaces, nonabelian Hodge spaces and global Lie theory

I will review some geometric aspects of the the wild character varieties. Whereas the exponential map from a Lie algebra to a Lie group can be viewed as the monodromy of a singular connection $A{\rm d}z/z$ on a disk, the wild character varieties are the receptacles for the monodromy data for arbitrary meromorphic connections on Riemann surfaces. Most of the familiar story in the tame case has now been extended to the wild case, and this makes contact with many applications.

## Quantum theta functions and signal analysis

Representations of the celebrated Heisenberg commutation relations and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In this talk I explain how Heisenberg relations bridge the noncommutative geometry and signal analysis. After providing a brief comparative dictionary of the two languages, I will show e.g.

## POSTER SESSION

For titles and abstracts of the posters, please see the attached pdf.

## "surprise"

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