# Lectures, seminars and dissertations

* Dates within the next 7 days are marked by a star.

Johanna Immonen (Helsinki University)

**Percolation and Modular Invariance**

*** Today * ** Tuesday 05 December 2023, 10:15, M3 (M234)

The talk will consider modular forms and crossing probabilities. In particular, I will review how Cardy's formula can be expressed in terms of the modular Eta function, and further, that Cardys function is the unique function that satisfies f(r)+f(1/r)=1 and has an expansion in form e−2παr times a power series in e−2πr for some α∈R. The first property is implied by a symmetry of the problem, but there is no physical argument for the latter.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Miryam Gnazzo

**Computing closest singular matrix-valued functions**

*** ** Thursday 07 December 2023, 09:15, M2 (M233)

Harri Hakula

Alexis Langlois-Rémillard (University of Bonn)

**Uncoiled periodic and affine Temperley-Lieb algebras, Jones-Wenzl projectors and their trace**

Tuesday 12 December 2023, 10:15, M3 (M234)

The affine and periodic Temperley-Lieb algebras are families of infinite-dimensional algebras with a diagrammatic presentation. They have been studied in the last 30 years, mostly for their physical applications in statistical mechanics, where the diagrammatic presentation encodes the connectivity property of the models. Most of the relevant representations for physics are finite-dimensional.
In the first part of the talk, we will present the diagrammatic calculus related to these algebras and define finite-dimensional quotients of these algebras, which we name uncoiled algebras in reference to the diagrammatic interpretation. Afterwards, we construct a family of Jones-Wenzl idempotents, each of which projects onto one of the one-dimensional modules these algebras admit.
The second part of the talk will go in depth on the construction of the Jones-Wenzl idempotents and present some of their applications, mainly looking at their trace.

Aalto mathematical physics seminar (Kytölä, Peltola, Sahlsten)

Prof. Ting Xue (University of Melbourne)

**Springer theory and finite groups of Lie type**

Tuesday 12 December 2023, 15:15, U6 KONECRANES (U149)

Springer theory for reductive algebraic groups plays an important role in determining irreducible characters of finite groups of Lie type. We discuss its generalisation to the setting of graded Lie algebras. We explain how level-rank dualities arise from unipotent irreducible characters and their connections with the graded Springer theory. If time permits, we discuss a conjectural realisation of these dualities using affine Springer fibers.

Thomas Wasserman (University of Oxford)

**TBA**

Tuesday 19 December 2023, 10:15, M3 (M234)

mathematical physics seminar (Kytölä, Peltola)

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