Videos and presentation materials from other INI events are also available.
Event  When  Speaker  Title  Presentation Material 

ARA 
18th March 2021 15:30 to 16:30 
Jonathan Chapman  Exponential asymptotics in applied mathematics  
ARA 
18th March 2021 17:00 to 18:00 
Sergei Gukov  The role of resurgence in QFT and in string theory  
ARAW01 
22nd March 2021 13:50 to 14:00 
Director of INI’s Welcome Talk  
ARAW01 
22nd March 2021 14:00 to 16:00 
Adri Olde Daalhuis, Christopher Howls  Stokes Phenomena: From Dingle to Exponential Asymptotics  
ARAW01 
22nd March 2021 16:00 to 17:00 
Gerald Dunne  Resurgence in Differential Equations, and Effective Summation Methods  
ARAW01 
23rd March 2021 14:00 to 15:00 
Adri Olde Daalhuis, Christopher Howls  Stokes Phenomena: From Dingle to Exponential Asymptotics  
ARAW01 
23rd March 2021 15:00 to 17:00 
Gerald Dunne  Resurgence in Differential Equations, and Effective Summation Methods  
ARAW01 
23rd March 2021 17:00 to 19:00 
Evening Tutorial  
ARAW01 
24th March 2021 14:00 to 15:00 
Philippe Trinh, John King, Jonathan Chapman  Exponential Asymptotics for Physical Applications  
ARAW01 
24th March 2021 15:00 to 16:00 
Kemal Gokce Basar  WKB, Eigenvalue Problems and Quantisation in QM  
ARAW01 
24th March 2021 16:00 to 17:00 
Daniele Dorigoni  Ecalle’s Theory of Resurgence  
ARAW01 
24th March 2021 17:00 to 19:00 
Evening Tutorial  
ARAW01 
25th March 2021 10:00 to 12:00 
Morning Tutorial  
ARAW01 
25th March 2021 14:00 to 15:00 
Philippe Trinh, John King, Jonathan Chapman  Exponential Asymptotics for Physical Applications  
ARAW01 
25th March 2021 15:00 to 16:00 
Kemal Gokce Basar  WKB, Eigenvalue Problems and Quantisation in QM  
ARAW01 
25th March 2021 16:00 to 17:00 
Daniele Dorigoni  Ecalle’s Theory of Resurgence  
ARAW01 
25th March 2021 17:00 to 19:00 
Evening Tutorial  
ARAW01 
26th March 2021 10:00 to 12:00 
Morning Tutorial  
ARAW01 
26th March 2021 14:00 to 15:00 
Philippe Trinh, John King, Jonathan Chapman  Exponential Asymptotics for Physical Applications  
ARAW01 
26th March 2021 15:00 to 16:00 
Kemal Gokce Basar  WKB, Eigenvalue Problems and Quantisation in QM  
ARAW01 
26th March 2021 16:00 to 17:00 
Daniele Dorigoni  Ecalle’s Theory of Resurgence  
ARA 
30th March 2021 16:00 to 17:00 
Michael Berry 
Differentiations and Diversions
Asymptotic procedures, such as generating slowness corrections to geometric phases, involve successive differentiations. For a large class of functions, the universal attractor of the differentiation map is, when suitably scaled, locally trigonometric/exponential; nontrivial examples illustrate this. For geometric phases, the series must diverge, reflecting the exponentially small final transition amplitude. Evolution of the amplitude towards this final velue depends sensitively on the representation used. If this is optimal, the transition takes place rapidly and universally across a Stokes line emanating from a degeneracy in the complex time plane. But some Hamiltonian ODE systems do not generate transitions; this is because the complexplane degeneracies have a peculiar structure, for which there is no Stokes phenomenon. Oscillating high derivatives (asymptotic monochromaticity) and superoscillations (extreme polychromaticity) are in a sense opposite mathematical phenomena. 

ARA 
1st April 2021 16:00 to 17:00 
Ovidiu Costin 
Optimal reconstruction of functions from their truncated power series at a point I will speak about the question of the mathematically optimal reconstruction of a function from a finite number of terms of its power series at a point, and on aditional data such as: as domain of analyticity, bounds or others. Aside from its intrinsic mathematical interest, this question is important in a variety of applications in mathematics and physics such as the practical computation of the Painleve transcendents, which I will use as an example, and the reconstruction of functions from resurgent perturbative series in models of quantum field theory and string theory. Given a class of functions which have a common Riemann surface and a common type of bounds on it, we show that the optimal procedure stems from the uniformization theorem. A priori Riemann surface information and bounds exist for the Borel transform of asymptotic expansions in wide classes of mathematical problems such as meromorphic systems of linear or nonlinear ODEs, classes of PDEs and many others, known, by mathematical theorems, to be resurgent. I will also discuss some (apparently) new uniformization methods and maps. Explicit uniformization in Borel plane is possible for all linear or nonlinear second order meromorphic ODEs. This optimal procedure is dramatically superior to the existing (generally adhoc) ones, both theoretically and in their effective numerical application, which I will illustrate. The comparison with Pade approximants is especially interesting. When more specific information exists, such as the nature of the singularities of the functions of interest, we found methods based on convolution operators to eliminate these singularities. The type of singularities is known for resurgent functions coming from many problems in analysis. With this addition, the accuracy is improved substantially with respect to the optimal accuracy which would be possible in full generality. Work in collaboration with G. Dunne, U. Conn. 

ARA 
8th April 2021 16:00 to 17:00 
Gergő Nemes 
Realistic error bounds for asymptotic expansions via integral representations We shall consider the problem of deriving realistic error 

ARA 
13th April 2021 16:00 to 17:00 
Mithat Unsal  From rainbow to mass gap: Resurgence and Lefschetz thimbles at work  
ARA 
15th April 2021 16:00 to 17:00 
Marcel Vonk  Matrix models; asymptotics, transesseries, theta functions and all that  
ARA 
20th April 2021 16:00 to 17:00 
John King 
Some PDEs and relatives
I shall describe the role of exponentially small terms in some PDEs and related differential difference equations, and ask questions about possible commonalities with QFTs. While I am mainly interested in dissipative (parabolic) cases, I shall  for reasons that are presumably obvious  focus on properties shared by the corresponding timereversible (hyperbolic) models. 

ARA 
22nd April 2021 16:00 to 17:00 
Christopher Howls  A More Exotic Asymptotic Zoo: New Stokes Lines, Virtual Turning Points and the Higher Order Stokes Phenomenon  
ARA 
27th April 2021 16:00 to 17:00 
Sheehan Olver 
Riemann–Hilbert problems and Stokes phenomena
Riemann–Hilbert problems consist of recovering a piecewise analytic function from information about jumps along branch cuts. To quote Wikipedia (as of today): "Stokes phenomenon, discovered by G. G. Stokes (1847, 1858), is that the asymptotic behaviour of functions can differ in different regions of the complex plane”. We demonstrate how Stokes phenomena can lead naturally to a Riemann–Hilbert problem which in fact uniquely determines the analytic function, beginning, of course, with everyone’s favourite example: the Airy function. We further review the applications to Painlevé equations, and finally show that integrals with coalescing saddles can also be reformulated as a Riemann–Hilbert problem, in a way that, perhaps, avoids the computational pitfalls of applying quadrature directly to integral reformulations along steepest descent contours 

ARA 
29th April 2021 08:00 to 09:00 
Yoshitsugu Takei 
Global study of differential equations via the exact WKB  from Schrödinger and Panlevé The exact WKB analysis provides a powerful tool for the 

ARA 
3rd May 2021 08:00 to 09:00 
Yasuyuki Hatsuda  Quantization conditions and SeibergWitten theory  
ARA 
4th May 2021 08:00 to 09:00 
Katsushi Ito  WKB periods for higher order ODE and TBA equations  
ARA 
5th May 2021 06:00 to 07:00 
Exact WKB vs resurgence in semiclassics Dr. Naohisa Sueishi  
ARA 
5th May 2021 08:00 to 09:00 
Degenerate Weber Stokes graph and its application  Dr. Syo Kamata  
ARA 
6th May 2021 10:00 to 11:00 
Gergő Nemes  Resurgent methods in exact WKB analysis  Discussion Leader Dr Gergő Nemes  
ARA 
6th May 2021 16:00 to 17:00 
Andrew Neitzke 
Exact WKB and abelianization of flat connections
I will discuss a geometric approach to the exact WKB method via "abelianization" of flat connections  replacing SL(N)connections over a Riemann surface by GL(1)connections over an Nfold branched cover  and relations to DonaldsonThomas invariants and cluster algebras. Most of the story is on solid footing for equations of order N=2 (the case of Schrodinger equations), and conjectural for higher N. 

ARA 
11th May 2021 16:15 to 17:15 
Michal P. Heller 
Resurgence in Relativistic Hydrodynamics: Bjorken Flow Results
Relativistic hydrodynamics is a classical field theory with dissipation. Significant contemporary interest in relativistic hydrodynamics comes from its central role in modelling nuclear collisions at RHIC and LHC, robust connections with gravity uncovered in the course of the past two decades, as well as more recent applications to neutron stars mergers. The ideas of transseries and resurgence in relativistic hydrodynamics appeared for the first time as a byproduct of studies of Bjorken flow in the context of nuclear collisions at RHIC and LHC. The talk will provide a pedagogical review of these developments, as well as it will try to put them in the context of other topics to be discussed during the focus week on resurgence in relativistic hydrodynamics. 

ARA 
13th May 2021 16:00 to 17:00 
Benjamin Withers 
From quasinormal modes to constitutive relations
I will review recent developments in largeorder relativistic hydrodynamics. Starting with properties gleaned from holographic theories and black hole physics, I will show that quasinormal mode dispersion relations have a finite radius of convergence set by branch points corresponding to 'mode collisions' in the complex momentum plane. I will explore the consequences of this observation for the hydrodynamic gradient expansion of the onepoint functions of currents, including the role played by initial data, the impact of nonlinearities, and the structure of transseries. 

ARA 
18th May 2021 14:00 to 15:00 
Alba Grassi  title tba  
ARA 
20th May 2021 11:00 to 12:00 
Nalini Joshi  title tba 