Seminars this week

Mathematical Biology Seminar

Enrico Dell'Arra (Sheffield)

Mon, 29 April at 13:00
Hicks J11

The Sheffield Geometry and Physics Seminar

Sukjoo Lee (Edinburgh)

Hodge number duality for orbifold Clarke mirror pairs via tropical geometry.

Mon, 29 April at 14:00
Hicks Seminar Room J11

Abstract

Hodge number duality is one of the most fundamental phenomena in mirror symmetry. In the 1990s, Batyrev and Borisov introduced a combinatorial mirror construction for nef toric complete intersections of Calabi-Yau varieties, verifying Hodge number duality for these cases. Clarke has recently expanded this construction, broadening its scope to include a wide range of examples of mirror pairs. In this talk, I will discuss ongoing work with Andrew Harder, where we establish Hodge number duality for a large class of orbifold Clarke mirror pairs. We achieve this by developing a new tropical geometric tool to compute Hodge numbers. Our results not only confirm the result of Batyrev and Borisov but also lead to a proof of a conjecture by Katzarkov, Kontsevich, and Pantev for orbifold toric complete intersections. If time permits, I will also describe several applications, including the functoriality in Fano mirror symmetry and mirror symmetry for singular varieties.

The Sheffield Geometry and Physics Seminar

Dylan Butson (Oxford)

W-algebras, Yangians, and Calabi-Yau threefolds

Mon, 29 April at 15:00
Hicks Seminar Room J11

Abstract

I'll recall some basics about Slodowy slices, generalized slices in the affine Grassmannian, and quantizations thereof called W-algebras and Yangians, respectively, as well as their analogues for affine Lie algebras which are naturally described using the theory of vertex algebras. Then I'll explain a construction of vertex algebras associated to divisors in toric Calabi-Yau threefolds, which include affine W-algebras in type A for arbitrary nilpotents, and outline a dictionary between the geometry of the threefolds and the representation theory of these algebras. I'll also explain the physical interpretation of these results, as an example of twisted holography for M5 branes in the omega background.

The Sheffield Geometry and Physics Seminar

Mon, 29 April at 16:00
Hicks Seminar Room J11

Number Theory seminar

Bence Hevesi (Kings College London)

Local-global compatibility at l=p for torsion automorphic Galois representations

Tue, 30 April at 13:00
Hicks Seminar Room J11 / Google Meet

Abstract

Some ten years ago, Scholze proved the existence of Galois representations associated with torsion eigenclasses appearing in the cohomology of locally symmetric spaces for GL_n over imaginary CM fields. Since then, the question of local-global compatibility for these automorphic Galois representations has been an active area of research motivated by applications towards new automorphy lifting theorems. I will report on my work on local-global compatibility at l=p in this direction, generalising the results of the celebrated 10-author paper and Caraiani—Newton.

Statistics Seminar

Tue, 30 April at 15:00
Hicks Seminar Room J11

ShEAF: postgraduate pure maths seminar

Tue, 30 April at 16:00
Hicks Seminar Room J11

Pure Maths Colloquium

David Corfield (University of Kent)

Wed, 1 May at 14:00
Hicks Seminar Room J11

SP2RC/ESPOS seminar

Sanja Danilovic (Institute for Solar Physics, Stockholm University, Sweden)

An overview of last October's SST-SolO observational campaign

Thu, 2 May at 10:00
Zoom

Abstract

We present the results of coordinated observations of the Swedish 1-m Solar Telescope with Solar Orbiter that took place from October 12th to 26th 2023. The campaign resulted in 7 datasets of various quality. The observational programs were adjusted to the seeing conditions. The observations cover two active regions and a coronal hole. We focus on the morphology and evolution of several targets that are observed from two vantage points. We share the lessons we learned and give an outline of our plans for October this year and the support we could give during remote sensing windows 16 and 17.

Web announcement:
https://espos.stream/2024/05/02/Danilovic/
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Zoom link: https://zoom.us/j/165498165
(Meeting ID: 165 498 165)

Topology Seminar

Ehud Meir (Aberdeen)

Invariants that are covering spaces and their Hopf algebras

Thu, 2 May at 16:00
Hicks Seminar Room J11

Abstract

Different flavours of string diagrams arise naturally in studying algebraic structures (e.g. algebras, Hopf algebras, Frobenius algebras) in monoidal categories. In particular, closed diagrams can be realized as scalar invariants. For a structure of a given type the closed diagrams form a commutative algebra that has a richer structure of a self dual Hopf algebra. This is very similar, but not quite the same, as the positive self adjoint Hopf algebras that were introduced by Zelevinsky in studying families of representations of finite groups. In this talk I will show that the algebras of invariants admit a lattice that is a PSH-algebra. This will be done by considering maps between invariants, and realizing them as covering spaces. I will then show some applications to subgroup growth questions, and a formula that relates the Kronecker coefficients to finite index subgroups of free groups.

Plasma Dynamics Group

Ellie Mcclure (Sheffield)

Thu, 2 May at 16:00
Room E39 (Hicks Building)