NCTS International Geometric Measure Theory Seminar

† Focuses on the regularity and singularity theories for submanifolds of Riemannian manifolds and some of their applications †

We envisage an event built around virtual presentations on progress in geometric measure theory by external speakers. Every researcher is free to register as a participant and thus gain access to a virtual facility which is complete with lobby, lecture hall, and areas with boards for discussion. Thus, it shall recreate the exchange possibilities found at international conferences. For registered participants, the discussion rooms and their boards can be used at all times.

News

New Venue

As Wonder was shut down, the seminar has been moved to HyHyve.
• The user experience is quite similar in general.
• Login is now email based instead of password based.
• Miro boards are yet more integrated into the venue.

Next Topic

Energy identity for stationary harmonic maps, Daniele Valtorta (University of Milano Bicocca)

Calendars available

Researchseminars.org provides the following calendar links:
• Google calendar
• iCal/Outlook

The links labeled Google Calendar or iCal/Outlook allow you to export the presentations of this seminar to your chosen calendar app. Later, when further presentations are added, your calendar will automatically be updated.

Organisers

Giovanni Alberti (University of Pisa)

Ulrich Menne (National Taiwan Normal University & National Center for Theoretical Sciences)

Yoshihiro Tonegawa (Tokyo Institute of Technology)

Neshan Wickramasekera (University of Cambridge)

Former organiser: Guido De Philippis (till March 2022, successor: Giovanni Alberti).

Virtual Venue

Premises

Our virtual venue is the HyHyve space NCTS iGMT seminar with various Miro boards. Access to the venue is based on the email address of registered participants to which a one-time password will be sent. Lectures are based on the virtual board of the lecture hall. Six further boards are available in the discussion rooms of our virtual venue.

Instructions for HyHyve & Miro

Summary

Employing the web browser based gathering platform HyHyve, we hope to seamlessly embed a broadcasted presentation into a time of social interaction in varying small groups. Presentations are broadcasted and shall be given using virtual whiteboard of the lecture hall. Questions during the talk can be raised via group chat—monitored by the chairperson. In-depth discussions can be carried out in small groups after the broadcasted presentation

HyHyve

Step 1: Setup your Name, Camera and Microphone

Step 2: The HyHyve Mechanic: Engage with others

Step 3: Your Profile

Miro

All virtual whiteboards are accessible via HyHyve or web browser upon entering the guest password; every participant can individually navigate and zoom. On the lecture hall whiteboard, participants have view-only access. On whiteboards in the discussion areas, participants can enter their name and edit the board. Writing on boards is best done by a pad.

Schedule

Wednesday, 15 May 2024, 8:00 p.m.-10:00 p.m. (Taipei time)

Title
Energy identity for stationary harmonic maps

Speaker
Daniele Valtorta (University of Milano Bicocca)

Abstract
We present the proof for Energy Identity for stationary harmonic maps. In particular, given a sequence of stationary harmonic maps weakly converging to a limit with a defect measure for the energy, then m ⎯２ almost everywhere on the support of this measure the density is the sum of energy of bubbles. This is equivalent to saying that annular regions (or neck regions) do not contribute to the energy of the limit.

This result is obtained via a quantitative analysis of the energy in annular regions for a fixed stationary harmonic map. The proof is technically involved, but it will be presented in simplified cases to try and convey the main ideas behind it. (Preprint available on arXiv:2401.02242)

Link
HyHyve space NCTS iGMT seminar (only for registered participants, opened 1 hour before the event).

Complete instructions are available above.

Local Time

Wednesday, 15 May 2024

Cambridge, UK
1:00 p.m.-3:00 p.m.

Milan
2:00 p.m.-4:00 p.m.

Taipei
8:00 p.m.-10:00 p.m.

Tokyo
9:00 p.m.-11:00 p.m.

Upcoming Presentations

Speakers and time are announced around two months before the date of the talk. Further seminars will take place at 15 May 2024, 17 Jul. 2024, 18 Sep. 2024, 20 Nov. 2024, 15 Jan. 2025.

Past Presentations

Thursday, 28 March 2024, 6:30-8:30 a.m. (Taipei time)

Title
On the Multiplicity One Conjecture for Mean Curvature Flows of Surfaces

Speaker
Richard Bamler ( University of California, Berkeley)

We prove the Multiplicity One Conjecture for mean curvature flows of surfaces in $\mathbb R^3$. Specifically, we show that any blow-up limit of such mean curvature flows has multiplicity one. This has several applications. First, combining our work with results of Brendle and Choi-Haslhofer-Hershkovits-White, we show that any level set flow starting from an embedded surface diffeomorphic to a 2-spheres does not fatten. In fact, we obtain that the problem of evolving embedded 2-spheres via the mean curvature flow equation is well-posed within a natural class of singular solutions. Second, we use our result to remove an additional condition in recent work of Chodosh-Choi-Mantoulidis-Schulze. This shows that mean curvature flows starting from any generic embedded surface only incur cylindrical or spherical singularities. Third, our approach offers a new regularity theory for solutions of mean curvature flows that flow through singularities.

This talk is based on joint work with Bruce Kleiner.

Wednesday, 10 January 2024, 8:30-10:30 p.m. (Taipei time)

Title
Uniformly rectifiable metric spaces

Speaker
Raanan Schul (Stony Brook University)

In their 1991 and 1993 foundational monographs, David and Semmes characterized uniform rectifiability for subsets of Euclidean space in a multitude of geometric and analytic ways. The fundamental geometric conditions can be naturally stated in any metric space and it has long been a question of how these concepts are related in this general setting. In joint work with D. Bate and M. Hyde, we prove their equivalence. Namely, we show the equivalence of Big Pieces of Lipschitz Images, Bi-lateral Weak Geometric Lemma and Corona Decomposition in any Ahlfors regular metric space. Loosely speaking, this gives a quantitative equivalence between having Lipschitz charts and approximations by nice spaces. After giving some background, we will explain the main theorems and outline some key steps in the proof (which will include a discussion of Reifenberg parameterizations). We will also mention some open questions.

Wednesday, 15 November 2023, 8:00-10:00 p.m. (Taipei time)

Title
Mean curvature flow with surgery

Speaker
Robert Haslhofer (University of Toronto)

Flows with surgery are a powerful method to evolve geometric shapes, and have found many important applications in geometry and topology. In this talk, I will describe a new method to establish existence of flows with surgery. In contrast to all prior constructions of flows with surgery in the literature, our new approach does not require any a priori estimates in the smooth setting. Instead, our approach uses geometric measure theory, building in particular on the work of Brakke and White. We illustrate our method in the classical setting of mean-convex surfaces in R3 , thus giving a new proof of the existence results due to Brendle-Huisken and Kleiner and myself. Moreover, our new method also enables the construction of flows with surgery in situations that have been inaccessible with prior techniques, including in particular the free-boundary setting.

Wednesday, 20 September 2023, 4:00-6:00 p.m. (Taipei time)

Title
Rectifiability, finite Hausdorff measure, and compactness for non-minimizing Bernoulli free boundaries

Speaker
Georg Weiss (University of Duisburg-Essen)

While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time-dependent problem occur naturally in applied problems such as water waves and combustion theory.

For such critical points u–which can be obtained as limits of classical solutions or limits of a singular perturbation problem–it has been open since [Weiss03] whether the singular set can be large and what equation the measure ∆u satisfies, except for the case of two dimensions. In the present result we use recent techniques such as a frequency formula for the Bernoulli problem as well as the celebrated Naber-Valtorta procedure to answer this more than 20 year old question in an affirmative way:

For a closed class we call variational solutions of the Bernoulli problem, we show that the topological free boundary ∂{u > 0} (including degenerate singular points x, at which u(x + r·)/r → 0 as r → 0) is countably H n-1-rectifiable and has locally finite H n-1-measure, and we identify the measure ∆u completely. This gives a more precise characterization of the free boundary of u in arbitrary dimension than was previously available even in dimension two.

We also show that limits of (not necessarily minimizing) classical solutions as well as limits of critical points of a singularly perturbed energy are variational solutions, so that the result above applies directly to all of them.

This is a joint work with Dennis Kriventsov (Rutgers).

Wednesday, 12 July 2023, 4:00-6:00 p.m. (Taipei time)

Title
Analysis of singularities of area minimizing currents

Speaker
Brian Krummel (University of Melbourne)

The monumental work of Almgren in the early 1980s showed that the singular set of a locally area minimizing rectifiable current T of dimension n and codimension ≥ 2 has Hausdorff dimension at most n − 2. In contrast to codimension 1 area minimizers (for which it had been established a decade earlier that the singular set has Hausdorff dimension at most n − 7), the problem in higher codimension is substantially more complex because of the presence of branch point singularities, i.e. singular points where one tangent cone is a plane of multiplicity 2 or larger. Almgren’s lengthy proof (made more accessible and technically streamlined in the much more recent work of De Lellis-Spadaro) showed first that the non-branch-point singularities form a set of Hausdorff dimension at most n − 2 using an elementary argument based on the tangent cone type at such points, and developed a powerful array of ideas to obtain the same dimension bound for the branch set separately. In this strategy, the exceeding complexity of the argument to handle the branch set stems in large part from the lack of an estimate giving decay of T towards a unique tangent plane at a branch point.

We will discuss a new approach to this problem (joint work with Neshan Wickramasekera). In this approach, the set of singularities (of a fixed integer density q) is decomposed not as branch points and non-branch-points, but as a set B of branch points where T decays towards a (unique) plane faster than a fixed exponential rate, and the complementary set S. The set S contains all (density q) non-branch-point singularities, but a priori it could also contain a large set of branch points. To analyze S, the work introduces a new, intrinsic frequency function for T relative to a plane, called the planar frequency function. The planar frequency function satisfies an approximate monotonicity property, and takes correct values (i.e. ≤ 1) whenever T is a cone (for which planar frequency is defined) and the base point is the vertex of the cone. These properties of the planar frequency function together with relatively elementary parts of Almgren’s theory (Dirichlet energy minimizing multivalued functions and strong Lipschitz approximation) imply that T satisfies a key approximation property along S: near each point of S and at each sufficiently small scale, T is significantly closer to some non-planar cone than to any plane. This property together with a new estimate for the distance of T to a union of non-intersecting planes and the blow-up methods of Simon and Wickramasekera imply that T has a unique non-planar tangent cone at H n-2-a.e. point of S and that S is (n − 2)-rectifiable with locally finite measure. Analysis of B using the planar frequency function and the locally uniform decay estimate along B recovers Almgren’s dimension bound for the singular set of T in a simpler way, and (again via Simon and Wickramasekera blow-up methods) shows that B (and hence the entire singular set of T ) is countably (n − 2)-rectifiable with a unique, non-zero multi-valued harmonic blow-up at H n-2-a.e. point of B.

Wednesday, 17 May 2023, 8:00-10:00p.m. (Taipei time)

Title
Generic regularity of minimizing hypersurfaces in dimensions 9 and 10

Speaker
Christos Mantoulidis (Rice University)

In joint work with Otis Chodosh and Felix Schulze we showed that the problem of finding a least-area compact hypersurface with prescribed boundary or homology class has a smooth solution for generic data in dimensions 9 and 10. In this talk I will explain the main steps of the proof.

Wednesday, 15 March 2023, 4:00-6:00p.m. (Taipei time)

Title
Bi-Lipschitz regularity of 2-varifolds with the critical Allard condition

Speaker
Jie Zhou (Capital Normal University)

Abstract
For an integral 2-varifold in the unit ball of the Euclidean space passing through the origin, if it satisfies the critical Allard condition, i.e., the mass of the varifold in the unit ball is close to the area of a flat unit disk and the L2 norm of the generalized mean curvature is small enough, we show that locally the support of the varifold admits a bi-Lipschitz parameterization from the unit disk. The presentation is based on a joint work with Dr. Yuchen Bi.

Wednesday, 18 January 2023, 9:00-11:00p.m. (Taipei time)

Title
Singularities, Rectifiability, and PDE-constraints

Speaker
Filip Rindler (University of Warwick)

Surprisingly many different problems of Analysis naturally lead to questions about singularities in (vector) measures. These problems come from both "pure" Analysis, such as the question for which measures Rademacher's theorem on the differentiability of Lipschitz functions holds, and its non-Euclidean analogues, as well as from "applied" Analysis, for example the problem to determine the fine structure of slip lines in elasto-plasticity. It is a remarkable fact that many of the (vector) measures that naturally occur in these questions satisfy an (under-determined) PDE constraint, e.g., divergence- or curl-freeness. The crucial task is then to analyse the fine properties of these PDE-constrained measures, in particular to determine the possible singularities that may occur. It turns out that the PDE constraint imposes strong restrictions on the shape of these singularities, for instance that they can only occur on a set of bounded Hausdorff-dimension, or even that the measure is k-rectifiable where its upper k-density is positive. The essential difficulty in the analysis of PDE-constrained measures is that many standard methods from harmonic analysis are much weaker in an L1-context and thus new strategies are needed. In this talk, I will survey recent and ongoing work on this area of research.

Wednesday, 23 November 2022, 9:00-11:00p.m. (Taipei time)

Title
The spherical Plateau problem: existence, uniqueness, stability

Speaker
Antoine Song (California Institute of Technology)

Consider a countable group G acting on the unit sphere S in the space of L2 functions on G by the regular representation. Given a homology class h in the quotient space S/G, one defines the spherical Plateau solutions for h as the intrinsic flat limits of volume minimizing sequences of cycles representing h. Interestingly in some special cases, for example when G is the fundamental group of a closed hyperbolic manifold of dimension at least 3, the spherical Plateau solutions are essentially unique and can be identified. However in general not much is known. I will discuss the questions of existence and structure of non-trivial Plateau solutions. I will also explain how uniqueness of spherical Plateau solutions for hyperbolic manifolds of dimension at least 3 implies stability for the volume entropy inequality of Besson-Courtois-Gallot.

Wednesday, 21 September 2022, 8:00-10:00 p.m. (Taipei time)

Title
Minimal hypersurfaces with cylindrical tangent cones

Speaker
Gábor Székelyhidi (Northwestern University)

I will discuss recent results on minimal hypersurfaces with cylindrical tangent cones of the form C × R, where C is a minimal quadratic cone, such as the Simons cone over S3 × S3. I will talk about a uniqueness result for such tangent cones in a certain non-integrable situation, as well as a precise description of such minimal hypersurfaces near the singular set under a symmetry assumption.

Wednesday, 20 July 2022, 8:00-10:00 p.m. (Taipei time)

Title
Hypersurfaces with prescribed-mean-curvature: existence and properties

Speaker
Costante Bellettini (University College London).

Let N be a compact Riemannian manifold of dimension 3 or higher, and g a Lipschitz non-negative (or non-positive) function on N. In joint works with Neshan Wickramasekera we prove that there exists a closed hypersurface M whose mean curvature attains the values prescribed by g. Except possibly for a small singular set (of codimension 7 or higher), the hypersurface M is C2 immersed and two-sided (it admits a global unit normal); the scalar mean curvature at x is g(x) with respect to a global choice of unit normal. More precisely, the immersion is a quasi-embedding, namely the only non-embedded points are caused by tangential self-intersections: around any such non-embedded point, the local structure is given by two disks, lying on one side of each other, and intersecting tangentially (as in the case of two spherical caps touching at a point). A special case of PMC (prescribed-mean-curvature) hypersurfaces is obtained when g is a constant, in which the above result gives a CMC (constant-mean-curvature) hypersurface for any prescribed value of the mean curvature.

Wednesday, 18 May 2022, 8:00-10:00 p.m. (Taipei time)

Title
(Non-)quantization phenomena for higher-dimensional Ginzburg-Landau vortices

Speaker
Alessandro Pigati (New York University, Courant Institute)

The Ginzburg-Landau energies for complex-valued maps, initially introduced to model superconductivity, were later found to approximate the area functional in codimension two.

While the pioneering works of Lin-Rivière and Bethuel-Brezis-Orlandi (2001) showed that, for families of critical maps, energy does concentrate along a codimension-two minimal submanifold, it has been an open question whether this happens with integer multiplicity. In this talk, based on joint work with Daniel Stern, we show that, in fact, the set of all possible multiplicities is precisely {1} U [2,∞).

Wednesday, 16 March 2022, 8:00-10:00 p.m. (Taipei time)

Title
A Regularity Theorem for Area-minimizing Currents at Higher Multiplicity Boundary Points

Speaker
Simone Steinbrüchel (Leipzig University)

Abstract
The boundary regularity theory for area-minimizing integral currents in higher codimension has been completed in 2018 by a work of De Lellis, De Philippis, Hirsch and Massaccesi proving the density of regular boundary points. In this talk, I will present our recent paper where we took a first step into analyzing area-minimizing currents with higher multiplicity boundary. This question has first been raised by Allard and later again by White. We focus on two-dimensional currents with a convex barrier and define the regular boundary points to be those around which the current consists of finitely many regular submanifolds meeting transversally at the boundary. Adapting the techniques of Almgren, we proved that every boundary point is regular in the above sense. This is a joint work with C. De Lellis and S. Nardulli.

Wednesday, 18 January 2022, 8:30-10:30 p.m. (Taipei time)

Title
A Structure Theory for Branched Stable Hyper-surfaces

Speaker
Paul Minter (University of Cambridge)

Abstract
There are few known general regularity results for stationary integral varifolds aside from Allard’s celebrated theory. The primary reason for this is the possibility of a degenerate type of singularity known as a branch point, where at the tangent cone level singularities vanish and are replaced with regions of higher multiplicity. In this talk I will discuss a recent regularity theory for branched stable hypersurfaces which do not contain certain so-called classical singularities, including new tangent cone uniqueness results in the presence of branch points. This theory can be readily applied to area minimising hypercurrents mod p, which resolves an old conjecture from the work of Brian White. Some results are joint with Neshan Wickramasekera.

Thursday, 18 November 2021, 6:00-8:00 a.m. (Taipei time)

Title
Stable minimal hypersurfaces in R^4

Speaker
Otis Chodosh (Stanford University)

Abstract
I will explain why stable minimal hypersurfaces in R^4 are flat. This is joint work with Chao Li.

Wednesday, 22 September 2021, 8:15-9:15 p.m. (Taipei time)

Title
Free boundary regularity in the Stefan problem

Speaker
Alessio Figa lli (ETH Zurich)

Abstract
The Stefan problem describes phase transitions, such as ice melting to water. In its simplest formulation, this problem consists of finding the evolution of the temperature off the water when a block of ice is submerged inside.

In this talk, I will first discuss the classical theory for this problem. Then I will present some recent results concerning the fine regularity properties of the interface separating water and ice (the so called "free boundary"). As we shall see, these results provide us with a very refined understanding of the Stefan problem's singularities, and they answer some long-standing open questions in the field.

Wednesday, 21 July 2021, 8:15-9:15 p.m. (Taipei Time)

Title
A non-linear Besicovitch–Federer projection theorem for metric spaces

Speaker
David Bate (University of Warwick)

Abstract
This talk will present a characterisation of purely n-unrectifiable subsets S of a complete metric space with finite n-dimensional Hausdorff measure by studying non-linear projections (i.e. 1-Lipschitz functions) into some fixed Euclidean space. We will show that a typical (in the sense of Baire category) non-linear projection maps S to a set of zero n-dimensional Hausdorff measure. Conversely, a typical non-linear projection maps an n-rectifiable subset to a set of positive n-dimensional Hausdorff measure. These results provide a replacement for the classical Besicovitch–Federer projection theorem, which is known to be false outside of Euclidean spaces.

Time permitting, we will discuss some recent consequences of this characterisation.

Wednesday, 19 May 2021, 9:30-10:30 p.m. (Taipei Time)

Title
Geometric Measure Theory: a powerful tool in Potential Theory

Speaker
Tatiana Toro (University of Washington)

Abstract
In this talk, I will describe a couple of instances in which ideas coming from geometric measure theory have played a central role in proving results in potential theory. Understanding limits of measures associated to second order divergence form operators has allowed us to establish equivalences between boundary regularity properties of solutions to these operators and the domains where they are defined.

Wednesday, 17 March 2021, 8:15-9:15 p.m. (Taipei Time)

Title
Mean Curvature Flow with Generic Initial Data

Speaker
Felix Schulze (University of Warwick)

Abstract
A well-known conjecture of Huisken states that a generic mean curvature flow has only spherical and cylindrical singularities. As a first step in this direction Colding-Minicozzi have shown in fundamental work that spheres and cylinders are the only linearly stable singularity models. As a second step toward Huisken's conjecture we show that mean curvature flow of generic initial closed surfaces in R^3 avoids asymptotically conical and non-spherical compact singularities. We also show that mean curvature flow of generic closed low-entropy hypersurfaces in R^4 is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact self-similarly shrinking solutions. This is joint work with Otis Chodosh, Kyeongsu Choi and Christos Mantoulidis.

Wednesday, 20 January 2021, 10:30-11:30 p.m. (Taipei Time)

Title
Second Order Estimates for Interfaces of Allen-Cahn

Speaker
Juncheng Wei (University of British Colombia)

Abstract
In this talk, I will discuss a uniform $C^{2, \theta}$ estimate for level sets of stable solutions to the singularly perturbed Allen-Cahn equation in dimensions $n \leq 10$ (which is optimal). The proof combines two ingredients: one is a reverse application of the infinite dimensional Lyapunov-Schmidt reduction method which enables us to reduce the $C^{2, \theta}$ estimate for these level sets to a corresponding one on solutions of Toda system; the other one uses a small regularity theorem on stable solutions of Toda system to establish various decay estimates, which gives a lower bound on distances between different sheets of solutions to Toda system or level sets of solutions to Allen-Cahn equation. (Joint work with Kelei Wang.)

Wednesday, 18 Nov. 2020, 6:00-7:00 a.m. (Taipei Time)

Title
Stable minimal hypersurfaces in $\R^{N+1+\ell}$ with singular set an arbitrary closed $K\subset\{0\}\times\R^{\ell}$.

Speaker
Leon Simon (Stanford University)

Abstract
With respect to a $C^{\infty}$ metric which is close to the standard Euclidean metric on $\R^{N+1+\ell}$, where $N\ge 7$ and $\ell\ge 1$ are given, we construct a class of embedded $(N+\ell)$-dimensional hypersurfaces (without boundary) which are minimal and strictly stable, and which have singular set equal to an arbitrary preassigned closed subset $K\subset\{0\}\times\R^{\ell}$.

Registration

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Participants

(Only those, who agreed to be listed on this page. )

Surname Given Name Affiliation

Aiex Nicolau University of Auckland

Aikawa Hiroaki Chubu University

Akagi Goro Tohoku university

Akahori Takafumi Shizuoka university

Akman Murat University of Essex

Alberti Giovanni University of Pisa

Alhawiti Noura Hamad M Newcastle University

Allard William Duke University

Alvarado Enrique Washington State University

Antonelli Gioacchino Scuola Normale Superiore, Pisa

Arora Rakesh Masaryk University

Arroyo Rabasa Adolfo Université catholique de Louvain

Ayoush Rami University of Warsaw

Babadjian Jean-Francois Paris Saclay University

Badran Marco University of Bath

Bae Junsik Ulsan National Institute of Science and Technology

Baik Hyungryul KAIST

Bansal Hemant Graduate Student

Bate David University of Warwick

Batista Marcio Federal University of Alagoas

Bellettini Costante University College London

Bernardini Chiara University of Padova

Bevilacqua Giulia Università di Pisa

Bi Yuchen University of Chinese Academy of Sciences

Blatt Simon University Salzburg

Bögelein Verena University of Salzburg

Bonicatto Paolo University of Warwick

Borza Samuël Durham University

Brena Camillo Scuola Normale Superiore

Buet Blanche Université Paris Saclay

Caldini Gianmarco University of Trento

Calisti Matteo The University of Bologna

Carazzato Davide Scuola Normale Superiore

Caselli Michele Scuola Normale Superiore

Castillo Victor Pontificia Universidad Catolica de Chile

Chang Claire Yun Ching NUK

Chang Chueh-Hsin Tunghai University

Chang Mao-Sheng Department of Mathemtics, Fu Jen Catholic University

Chen Chih-Wei National Sun Yat-Sen University

Chen GuanRu National Taiwan University

Chen Wan-Jhen Tamkang University

Chen Yen-Yu National Taiwan University

Chen Yikai Rice University

Chen Yi-Xian National Taiwan University

Cheng Jih-Hsin Academia Sinica

Chern Jann-Long National Taiwan Normal University

Chiang Robinson National Sun Yat-Sen University

Chihara Ryohei University of Tokyo

Chiu Sheng-Fu Academia Sinica

Chiu Shih-Kai University of Notre Dame

Chou Hsin-Chuang National Taiwan Normal University

Clara Gabriel University of Twente

Colombo Giulio University of Milano

Cooney Hugh The Australian National University

Correa Julio Catholic University of Rio de Janeiro

Cortopassi Tommaso Scuola Normale Superiore

Dahmani Abdelhakim University of Science and Technology Houari Boumediene, Algeria

Dai Jia-Yuan National Chung-Hsing University

Das Tushar University of West London

Deng Jialong Univeristy of Goettingen

De Fazio Paolo Università degli Studi di Parma

De Giorgio Lea University of Trento

De Lellis Camillo Institute for Advanced Study

De Masi Luigi Scuola Internazionale Superiore di Studi Avanzati (SISSA)

De Oliveira Reinaldo Resende University of São Paulo

De Pauw Thierry East China Normal University

De Queiroz Olivaine Senac SP

De Rosa Antonio University of Maryland

Dey Sarkar Debjit University of North Bengal

Dierkes Ulrich Universität Duisburg-Essen

Ding Qi Shanghai Center for Mathematical Sciences, Fudan University

Domazakis Georgios University of Sussex

Du Geyang Peking University

Duzaar Frank Department of Mathematics, University Erlangen-Nuremberg

Edelen Nick University of Notre Dame

Engelstein Max University of Minnesota

El-Hindi Mohammad Beirut Arab University

Eriksson-Bique Sylvester University of Oulu

Fang Yangqin Huazhong University of Science and Technology

Ferreri Lorenzo Scuola Normale Superiore

Fiorani Francesco University of Oxford

Fischer Simon-Raphael National Center for Theoretical Sciences

Fleschler Ian Princeton University

Florin Catrina St. John's University

Fogagnolo Mattia Centro De Giorgi, Scuola Normale Superiore

Friedrich Alexander University of Copenhagen

Fu Joe University of Georgia

Fu Ser-Wei National Center of Theoretical Sciences, NTU

Furukawa Ken RIKEN

Gasparetto Carlo Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste

Gazwani Mashniahi Newcastle University

Gelli Maria Stella Università di Pisa

Ghinassi Silvia University of Washington

Ghosh Sayan Ramakrishna Mission Vidyamandira Belur Math, Calcutta University

Gianniotis Panagiotis National and Kapodistrian University of Athens

Gianocca Matilde ETH

Giga Yoshikazu Univesity of Tokyo

Giovagnoli Davide Università di Bologna

Goering Max University of Washington

González Nevado Alejandro Universität Konstanz

Granuccci Tiziano Istituto Superiore Leonardo da Vinci

Gu Zhongyang The University of Tokyo

Guarino Lo Bianco Serena University of Naples "Federico II"

Guijarro Luis Instituto de Ciencias Matemáticas, ICMAT

Guo Changyu Shandong University

Haghshenas Mahdi University College London

Han Xiaolong California State University, Northridge

Harada Junichi Akita University

Hardt Robert Rice University

Hiesmayr Fritz SNS Pisa

Hirsch Jonas Universität Leipzig

Hirsch Sven Duke University

Ho Nan-Guo National Tsing Hua University

Honda Shouhei Tohoku University

Hong Han University of British Columbia

Horihata Kazuhiro Tohoku University

Hou Yu-Chi University of Maryland

Hsia Chun-Hsiung National Taiwan University

Hsu Chi-Yo National Tsing Hua University

Hsueh Chun-Sheng National Taiwan University

Hu Jingchen University of Science and Technology of China

Huang Chih-Chiang Chung Cheng University

Huang Hsin-Yuan National Chiao-Tung University

Huang Lan-Hsuan University of Connecticut

Huang Yen-Chang National University of Tainan

Hui Kin Ming Institute of Mathematics, Academia Sinica

Idu Kennedy Universita di Pisa

Ilmanen Tom ETH Zürich

Jeong Seonghyeon Michigan State University

Jiang Xuyong Changzhou University

Julia Antoine Université Paris-Saclay

Kagaya Takashi Kyushu University

Kalhori Mohsen Sharif University of Technology

Kang Hyunsuk Gwangju Institute of Science and Technology (GIST)

Kao Wei-Ting National Taiwan University

Katsuda Atsushi Kyushu university

Karpukhin Mikhail California Institute of Technology

Ketterer Christian University of Toronto

Khaitan Ayush Penn State University

Kim Ken LLNL/UC Berkeley

Kim Seongtag Inha University

Kimura Masato Kanazawa University

Koide Syota National Institute for Educational Policy Research

Kolasiński Sławomir Uniwersytet Warszawski

Krummel Brian University of Melbourne

Kuo Ting-Ting NCTS

Kwong Kwok Kun University of Wollongong

Labourie Camille University of Cyprus

Lamm Tobias Karlsruhe Institute of Technology (KIT)

Larson Simon California Institute of Technology

Laux Tim University of Bonn

Lee Hojoo Jeonbuk National University

Lee Man-Chun The Chinese University of Hong Kong

Lee Niann-Chern National Chin-Yi University of Technology

Lee Tang-Kai MIT

Lee Yng-Ing National Taiwan University

LeFloch Philippe G. Sorbonne Université

Leitner Marianne Dublin Institute for Advanced Studies & abberior Instruments GmbH

Leskas Konstantinos UCL

Lesniak Maciej University of Warsaw

Li Martin Man-Chun The Chinese University of Hong Kong

Li Rusen Shandong University

Li Yangyang Princeton University

Li Zhuolin University of Oxford

Liang Xiangyu Beihang University

Lin Chun-Chi National Taiwan Normal University

Lin Longzhi University of California, Santa Cruz

Lin Yi-Hsuan National Yang Ming Chiao Tung University

Liu Yu Tong National Taiwan Normal University

Lubbe Felix University of Copenhagen

Luchese Mattia University of Cambridge

Lymberopoulos Alexandre Universidadde de São Paulo

Luo Wei Sichuan University

Ma John University of Copenhagen

Maggi Francesco University of Texas at Austin

Malchiodi Andrea Scuola Normale Superiore

Mangalath Vishnu Australian National University

Marchenko Ilya University of Notre Dame

Marchese Andrea University of Trento

Marshall-Stevens Kobe UCL

Masnou Simon Claude Bernard University Lyon 1

Matsuo Shinichiroh Nagoya University

McCormick Stephen Uppsala University

McCurdy Sean Carnegie Mellon University

Merlo Andrea Université Paris-Saclay

Merlino Enzo Maria University of Bologna

Minadakis Alexandros

Minarcik Jiri Czech Technical University in Prague

Mingione Giuseppe University of Parma

Minter Paul Princeton University

Miśkiewicz Michał Polish Academy of Sciences

Miura Tatsuya Tokyo Institute of Technology

Miyanishi Yoshihisa Shinshu University

Mizuno Masashi Nihon University

Møller Niels Martin University of Copenhagen

Mondino Andrea University of Oxford

Moon Sanghyuck National Center for Theoretical Sciences

Morgan Frank Williams College

Mori Ryunosuke Tokyo Institute of Technology

Moritoh Shinya Nara Women‘s University

Muhammad Ali University of Copenhagen

Nardulli Stefano CMCC-UFABC, Santo André, SP, Brazil

Nath Arijit IIT Madras

Nenciu Andrei Valentin Featurespace

Niu Gongping University of California, San Diego

Nguyen Le Tram National Taiwan Normal University

Nguyen Tien Université libre de Bruxelles

Niang Alassane Cheikh Anta Diop University of Dakar (Senegal)

Nova Paolo Bayes Business School

O'Hara Jun Chiba University

Ohsawa Takeo Nagoya University

Okamoto Jun The University of Tokyo

Onodera Michiaki Tokyo Institute of Technology

Ooi Yuan Shyong Pusan National University

Orlando Gianluca Politecnico di Bari

Oronzio Francesca Università degli studi di Roma

Pallardó-Julià Vicent Universitat de València

Parise Davide University of Cambridge

Park Jiewon Yale University

Park Jung-Tae Korea Institute for Advanced Study

Parker Phil Wichita State University

Pati Ashis IISER KOLKATA

Paxton Laramie Marian University–Wisconsin

Perales Raquel Institute of Mathematics at the National Autonomous University of Mexico