Classical Function Theory in Modern Mathematics

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Classical Function Theory in Modern Mathematics

 01 - 05 Jul 2024

ICMS, Bayes Centre, Edinburgh

 Enquiries

  • Lasse Rempe, University of Liverpool
  • Vasiliki Evdoridou, The Open University
  • Eugenia Malinnikova, Stanford University
  • Sergiy Merenkov, City College of New York
  • David Martí-Pete, University of Liverpool
  • Byung-Geun Oh, Hanyang University

About:

This workshop explored applications of classical function theory within modern mathematics. It brought together researchers from a diverse collection of mathematical fields, whose common ground was that they used function theory to make major progress in their area of study.

These participants might not usually interact, but would be able to communicate mathematically due to their shared background in complex analysis, providing fertile ground for fruitful new interactions between subjects, and thereby for fundamental progress in many areas of mathematics.

The timing of the workshop had been chosen to also celebrate the 70th birthday of Professor Alexandre Eremenko (Purdue University), a world leader in function theory whose work had a profound influence on a wide range of disciplines, including the theory of meromorphic functions, differential equations, dynamical systems, geometry (both differential and algebraic), potential theory, holomorphic curves, and theoretical physics.

We were very grateful for the support from ICMS, the National Research Foundation of Korea, and the Edinburgh Mathematical Society.

We were grateful to Springer for providing a copy of the book Research Problems in Function Theory: Fiftieth Anniversary Edition by Walter Hayman and Eleanor Lingham as the prize for the poster competition.

 

Programme

MONDAY 01 JULY 2024: Differential Equations
Registration and Refreshments
Welcome and Housekeeping
Alan Sokal, University College London Some conjectures concerning the zeros of the deformed exponential function
Refreshments
Eveliina Peltola, Aalto University and University of Bonn On geometric properties of conformally invariant curves
Lunch
Lakshmi Priya, Tel Aviv University Almost sharp lower bound for the nodal volume of harmonic functions
Masaki Tsukamoto, Kyoto University Rate distortion dimension of random Brody curves
Refreshments
Patrick Ng, University of Hong Kong Brody holomorphic curves on the degree six Fermat surface
Drinks reception & poster session
TUESDAY 02 JULY 2024: Complex Dynamics
Walter Bergweiler, University of Kiel The escaping set
Refreshments
Gwyneth Stallard, Open University Shrinking targets and recurrent behaviour for forward compositions of inner functions
Lunch
James Waterman, Stony Brook University A counterexample to Eremenko's conjecture
Melkana Brakalova-Trevithick, Fordham University When the circular dilatation at a point equals one
Refreshments
Mitsuhiro Shishikura, Kyoto University Reconstructing the dynamics via dynamical charts from a sequence of near-parabolic or cylinder renormalization
Public Lecture, hosted in G.03 (ground floor)
WEDNESDAY 03 JULY 2024: Geometry
Mario Bonk, UCLA Lamé functions and special elliptic integrals
Refreshments
Ilmari Kangasniemi, University of Cincinnati On the theory of quasiregular values
Yilin Wang, IHES Jordan curves with the piecewise geodesic property
Lunch and free afternoon
THURSDAY 04 JULY 2024: Meromorphic Functions
Mikhail Sodin, Tel Aviv University Equivariant Weierstrass theorem
Refreshments
Aimo Hinkkanen, University of Illinois Urbana-Champaign Moments and positivity
Lunch
Adi Glucksam, Northwestern University Multi-fractal spectrum of planar harmonic measure
Oleg Ivrii, Tel Aviv University Critical values of inner functions
Refreshments
Problem session, chair: Phil Rippon
Workshop Dinner
FRIDAY 05 JULY 2024: Geometry
Dmitri Panov, King's College London Spherical surfaces and their moduli spaces
Refreshments
Andrei Gabrielov, Purdue University Classification of generic spherical quadrilaterals
Lunch and End of Workshop

Sponsors and Funders:

  • NRF
  • EMS