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Invited Speakers

 Plenary Lectures

October 4 (Thu)

Prof. Tobias Weth
(Goethe-University Frankfurt)
October 4 (Thu) 10:20~11:10

Title: Curves and surfaces with constant nonlocal mean curvature
The notion of nonlocal mean curvature was introduced around 10 years ago and arises in variational problems for the fractional perimeter and related nonlocal interfacial energies. I will first review this notion and discuss its main properties in comparison with classical mean curvature. The main part of the talk will then focus on the class of hypersurfaces with constant nonlocal mean curvature. Although this class is still largely unexplored, first results show both similarities and striking differences to the classical local setting of constant mean curvature surfaces.

[This is joint work with Xavier Cabré (Universitat Politècnica de Catalunya, Barcelona), Mouhamed Moustapha Fall (AIMS Senegal, Mbour), Joan Solà-Morales (Universitat Politècnica de Catalunya, Barcelona).]


Prof. Jae Choon Cha
(Pohang University of Science and Technology)
October 4 (Thu) 11:10~12:00

Title: Hirzebruch-type L2-signature defects and topology of dimension 3 and 4
In 1968, Hirzebruch defined a signature defect invariant of manifolds over the group of order two, which was later generalized by many authors including Atiyah, Patodi, Singer, Wall, Cheeger and Gromov. I will discuss some recent advances in low dimensional topology, in which Hirzebruch-type L2-signature defects play an essential role. These will include the disk embedding problem in dimension 4, for topological and smooth cases, and quantitative topology of 3-manifolds.


October 5 (Fri)

Prof. Kenneth A. Ribet
(University of California, Berkeley)
October 5 (Fri) 10:20~11:10

Title: The Eisenstein ideal in the theory of modular curves and their Jacobian varieties
Barry Mazur’s celebrated 1977 article "Modular curves and the Eisenstein ideal" centers on the simplest modular curve, $X_0(N)$, where $N$ is a prime number.  In Mazur’s situation, the Eisenstein ideal has at least a half-dozen equivalent definitions because the ideal is the precise annihilator of a handful of physical objects attached to the modular curve.  In more general situations, mimicking the definitions in the prime-level case would lead to a collection of disparate ideals, and one can see easily in examples.  Nevertheless, there is a natural candidate for "Eisenstein ideal" that is contained in all the other candidates.  We show that this candidate is very close to being the exact annihilator of the cuspidal subgroup that was studied by Kubert and Lang in the 1970s and 1980s.  This is joint work with B. Jordan and A. Scholl.

Prof. Karl-Theodor Sturm
(Institute for Applied Mathematics, University of Bonn)
October 5 (Fri) 11:10~12:00

Title: Optimal transport, heat flow, and Ricci curvature on metric measure spaces
We present a brief survey on the theory of metric measure spaces with synthetic lower Ricci bounds, initiated by the author and by Lott/Villani, and developed further by Ambrosio/Gigli/Savare and by many others. Particular emphasis will be given to recent breakthroughs concerning the local structure of RCD-spaces by Mondino/Naber and by Brue/Semola and to rigidity results. For instance, given an arbitrary RCD(N-1,N)-space $(X,d,m)$, then $$\int\int \cos d(x,y)\, dm(x)\, dm(y)\le0$$ if and only if N is an integer and $(X,d,m)$ is isomorphic to the N-dimensional round sphere.
Moreover, we study the heat equation on time-dependent metric measure spaces and its dual as gradient flows for the energy and for the Boltzmann entropy, resp. Monotonicity estimates for transportation distances and for squared gradients will be shown to be equivalent to the so-called dynamical convexity of the Boltzmann entropy on the Wasserstein space which is the defining property of super-Ricci flows. Moreover, we show the equivalence with the monotone coupling property for pairs of backward Brownian motions as well as with log Sobolev, local Poincare and dimension free Harnack inequalities.

October 6 (Sat)

Prof. David Damanik
(Rice University)
October 6 (Sat) 10:20~11:10

Title: The KdV equation with almost periodic initial data 
Percy Deift has conjectured that solutions to the KdV equation with almost periodic initial data exist globally and are almost periodic in time. This talk will present the history and context of the problem, and explain recent work related to the Deift conjecture, especially in cases where the initial data in question are reflectionless. Within this class of initial data, the conjecture has been confirmed under suitable additional assumptions, but the resulting setup that establishes almost periodicity in time also suggests which mechanisms may be responsible for the potential existence of counterexamples.

Prof. Sung Yeon Kim
(Korea Institute for Advanced Study-CMC)
October 6 (Sat) 11:10~12:00

Title: $\bar \partial$-Neumann problem and effective termination of Kohn algorithm for subelliptic multipliers
In 1979, J.J. Kohn invented a purely algebraic construction of ideals of subelliptic multipliers for the $\bar\partial$-Neumann problem. But Kohn's original procedure gives no effective bound on the order of subellipticity in subelliptic estimates. In 2010, Y.-T. Siu obtained a new effective procedure to terminate Kohn’s algorithm for so-called special domains and outlined an extension of the special domain approach to general real-analytic and smooth cases. In this talk, we explain effective algorithm for multipliers and its difference with the full-real-radical Kohn algorithm. Then we propose a new class of geometric invariants, called jet vanishing orders, that permits us to obtain a new control of the effectiveness in the Kohn's construction procedure of subelliptic multipliers for the special domains of finite D'Angelo type in $\mathbb{C}^3$. We also present a triangular system of multipliers for special domain in arbitrary dimension. This is a joint project with D. Zaitsev.

 KIAS Public Lectures 

Prof. Hyungju Park
(Ajou University)
October 3 (Wed) 16:00~16:50

Title: How to tame massive data in an uncertain world
We live in an uncertain world, and face massive data everyday. Conspiracy theories are abound and propagate with the aid of SNS. There must be a way of navigating the torrent waves of big data!
Mathematics plays a key role in dealing with the uncertainly and the massiveness. It provides ways of telling significant information from insignificant one (the concept of entropy). Topology, a branch of mathematics, allows us to look at the shape of data in order to gain valuable insights about the nature of data.

Prof. Jürgen Richter-Gebert
(Technical University of Munich)
October 3 (Wed) 17:00~18:10

Title: Visualising Symmetry: A journey on the border of art and math
Symmetric structures are literally everywhere:
Nature produces (almost) symmetrical patterns.
Artefacts of cultures all over the world make use of repetitive patterns.
And in science symmetry can be found as an ordering principle.
Visual symmetric patterns (Ornaments) are full of amazing structures and surprising twists. The talk gives a mathematical view on the topic of visual symmetry starting from simple kaleidoscopic patterns via intricate circle limits a la M.C. Escher to complex non-Euclidean spaces. It shows the ups and downs the challenges and successes of the creation of software that allows a playful approach to this fascinating topic. The talk includes many interactive visual software demonstrations with state of the art software on tablets and computers and shows how virtual creations can turn into real world objects. It also gives insights into the vivid interplay of serious mathematics and playful art as well as playful mathematics and serious art.