Date/Time : 01 Jan 1970 10:00
Venue : TBA
Speaker : Yixuan Wang, Caltech

We drew inspiration from the Kolmogorov–Arnold representation theory, using a composition of sum of 1D functions to represent higher dimensional functions, and proposed KANs, which has learnable activation functions parameterized by splines. Compared with MLPs, it will have much better scaling laws and interpretability since we use a much smaller network with 1D functions, provided that the underlying function has such a smooth representation, and in practice we can make KANs arbitrarily wide and deep. We demonstrate the wide applicability of this paradigm by examples of function pitting, PDE solving (PINNs), and applications to scientific problems. I will also discuss the most up-to-date developments of KANs and present some theoretical understandings

Add to calendar :

Date/Time : 01 Jan 1970 14:00
Venue : S17 #04-06 (SR1)
Speaker : Zhang Tengren, National University of Singapore

Anosov subgroups are a special class of discrete subgroups of a non-compact semisimple Lie group. This notion was first discovered by Labourie, who used it to prove the discreteness of Hitchin representations. In this talk, I will discuss my recent contributions to our understanding of Anosov subgroups and their various generalizations, as well as some applications to studying character varieties.

Add to calendar :

Date/Time : 01 Jan 1970 16:15
Venue : S17 #04-05 (SR2)
Speaker : Trung Tuyen Truong, University of Oslo

This talk presents a new equivalence and approach to the Riemann hypothesis, via a relatively new root finding method called Backtracking New Q-Newton’s method (BNQN), which is a variant of Newton’s method. Besides having strong global guarantee for finding roots of meromorphic functions, this new method also has connections to Voronoi’s diagrams, which is an important input for the new approach. This is joint work with Thuan Quang Tran (University of Oslo).  

Add to calendar :

Date/Time : 01 Jan 1970 15:00
Venue : TBC
Speaker : Daniel Bartl, University of Vienna

A major challenge in modern optimization problems is their instability, where small data perturbations can have disproportionately significant effects. We address this challenge in two settings. First, we focus on a distributionally robust approach, a popular method to counteract instability generically using optimal transport. Specifically, we demonstrate how this approach can systematically quantify the (in-)stability of a given optimization problem. In the second part, we focus on statistical robustness, dealing with data subject to outliers, such as those caused by adversarial corruption. We design robust estimators for optimization problems and risk measures.

Add to calendar :

Date/Time : 01 Jan 1970 14:00
Venue : S17 #04-05 (SR2)
Speaker : Yongnam Lee, KAIST, Korea

In this talk, I will discuss the positivity of the tangent bundle of smooth projective surfaces. The first part of the talk will be focused on the classification of non-ruled surfaces with pseudo-effective tangent bundles, which is a joint work with Jia Jia and Goulei Zhong. The second part will be focused on weak del Pezzo surfaces with big tangent bundles. The bigness of the tangent bundle is expected to be determined through the configuration of (−2)-curves. Our approach is to produce irreducible effective divisors on the projectivized tangent bundle, called the total dual VMRT, associated to a conic fibration on weak del Pezzo surfaces.

This part is a joint work with Hosung Kim and Jeong-Seop Kim.

Add to calendar :

Date/Time : 01 Jan 1970 15:00
Venue : S17 #04-05 (SR2)
Speaker : Armin Schikorra, University of Pittsburgh

n-Laplace systems with antisymmetric potential are known to govern geometric equations such as n-harmonic maps between manifolds and generalized prescribed H-surface equations. Due to the nonlinearity of the leading order n-Laplace and the criticality of the equation they are very difficult to treat.

I will discuss some progress we obtained, combining stability methods by Iwaniec and nonlinear potential theory for vectorial equations by Kuusi-Mingione.

Joint work with Dorian Martino

Add to calendar :

Date/Time : 01 Jan 1970 14:00
Venue : S17 #04-05 (SR2)
Speaker : Jan M. Swart, The Czech Academy of Sciences

In a classical game two players, Alice and Bob, take turns to play n moves each. Alice starts. For each move each player has two options, 1 and 2. The outcome is determined by the exact sequences of moves played by each player. Prior to the game, a winner is assigned to each of the 2^{2n} possible outcomes in an i.i.d. fashion, where p is the probability that Bob is the winner for a given outcome. Then it is known that there exists a value 0<p_c<1 such that the probability that Bob has a winning strategy for large n tends to one if p>p_c and to zero if p<p_c. We study a modification of this game for which the outcome is determined by the exact sequence of moves played by Alice as before, but in the case of Bob all that matters is how often he has played move 1. We show that also in this case, there exists a sharp threshold p’_c that determines which player has with large probability a winning strategy in the limit as n tends to infinity.

Joint work with Anja Sturm and Natalia Cardona-Tob\’on (G\”ottingen).

Add to calendar :

Date/Time : 01 Jan 1970 15:00
Venue : S17 #04-05 (SR2)
Speaker : Min XU, Carnegie Mellon University

Cryo-electron tomography (cryo-ET) 3D imaging technology captures a 3D image of a single cell’s subcellular structures at sub-molecular resolution and in a near-native state. It provides unprecedented opportunities for systematically studying the native spatial organization of subcellular structures, especially macromolecules. However, cryo-ET has high structural complexity and imaging limits, such as high structural diversity and crowding, low signal-to-noise ratio, and missing values. These have made the automated systematic analysis of such images extremely difficult. I will present our recent efforts to develop methods for automated analysis of cryo-ET data.

Add to calendar :