* Seuraavan viikon tapahtumat merkitty tähdellä
Jinwoo Sung (Chicago)
Loewner energy reversibility revisited
* Tuesday 10 September 2024, 10:15, M3 (M234)
The Loewner energy of a chord in a simply connected domain is defined as the Dirichlet energy of the driving function for the corresponding Loewner chain. In a pioneering work, Yilin Wang identified Loewner energy as the large deviation rate function for chordal Schramm--Loewner evolution as the parameter κ decreases to 0. With this interpretation, she deduced from the reversibility of chordal SLE that the Loewner energy or a chord does not depend on reversing its orientation. I will present a deterministic proof of this fact by reversing the chord in small increments, highlighting similarities and differences from Dapeng Zhan's proof of SLE reversibility.
Mathematical Physics
Prof. Martin Lotz (University of Warwick)
Pfaffian Incidence Geometry and Applications
* Tuesday 10 September 2024, 15:15, M1 (M232)
Pfaffian functions are real or complex analytic functions that satisfy triangular systems of first-order partial differential equations with polynomial coefficients. Pfaffian functions, and by extension Pfaffian and semi-Pfaffian sets, play a crucial role in various areas of mathematics. Incidence combinatorics has recently experienced a surge of activity, fuelled by the introduction of the polynomial partitioning method of Guth and Katz. While traditionally restricted to simple geometric objects such as points and lines, focus has shifted towards incidence questions involving higher dimensional algebraic or semi-algebraic sets. We present a generalization of the polynomial partitioning method to semi-Pfaffian sets and illustrate how this leads to generalizations of classic results in incidence geometry, such as the Szemerédi-Trotter Theorem. Finally, we outline an application of semi-Pfaffian geometry to the robustness of neural networks.
Masashi Misawa
On regularity for doubly nonlinear parabolic type equations by the positivity-expansion
Wednesday 18 September 2024, 10:15, M3 (M234)
We shall consider the second-ordered partial differential equations of parabolic type, which have the p-Laplacian operator and the time-derivative of power-nonlinearity. We call the equations the doubly nonlinear parabolic type equations. Some interactions of fast and slow diffusions may appear and have some effect on regularity of solutions. Our aim is to study the regularity of weak solutions. It is generally necessary to treat sign-changing solutions because the equations considered here are not translation-invariant on unknown functions. We modify the so-called expansion of positivity to obtain the decay of local oscillation of sigh-changing solutions. Our method simplifies the previous proof of regularity in the fast-fast diffusion case and leads to the boundary regularity.
Seminar on analysis and geometry
Maxwell Forst
On the geometry of lattice extensions
Wednesday 18 September 2024, 16:15, M3 (M234)
Given a lattice L, an extension of L is a lattice M of strictly greater rank such that the intersection of M and the subspace spanned by L is equal to L. In this talk we will discuss constructions of such lattice extensions where particular geometric invariants of M, such as the determinant, covering radius and successive minima, are related the corresponding geometric invariants of L. This talk is based on joint work with Lenny Fukshansky.
ANTA Seminar / Hollanti et al.
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 04 October 2024, 09:00, M3 (M234)
Further information
Sari Rogovin
TBA
Wednesday 23 October 2024, 10:15, M3 (M234)
We shall consider the second-ordered partial differential equations of parabolic type, which have the p-Laplacian operator and the time-derivative of power-nonlinearity. We call the equations the doubly nonlinear parabolic type equations. Some interactions of fast and slow diffusions may appear and have some effect on regularity of solutions. Our aim is to study the regularity of weak solutions. It is generally necessary to treat sign-changing solutions because the equations considered here are not translation-invariant on unknown functions. We modify the so-called expansion of positivity to obtain the decay of local oscillation of sigh-changing solutions. Our method simplifies the previous proof of regularity in the fast-fast diffusion case and leads to the boundary regularity.
Seminar on analysis and geometry
Matematiikan kandiseminaari (Bachelor thesis seminar in Math.)
Friday 15 November 2024, 09:00, M3 (M234)
Further information
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