Date/Time : 27 Mar 2025 16:00
Venue : S17 #06-11 (SR6)
Speaker : Jiuzu Hong, University of North Carolina at Chapel Hill

Global Schubert varieties of parahoric Bruhat-Tits group schemes were introduced by Xinwen Zhu in his proof of the coherence conjecture of Pappas-Rapoport. These global Schubert varieties provide flat families relating spherical Schubert varieties in affine Grassmannians and other Schubert varieties or their unions in partial affine flag varieties. In a series of talks, I will give an introduction to this topic and discuss several applications based on my own research.

In the first talk, I will cover the basics of affine Grassmannian and Schubert varieties.
In the second talk, I will discuss parahoric group schemes and flag varieties of loop groups.
In the last talk, I will introduce the global Schubert varieties of parahoric Bruhat-Titis group schemes and discuss some of their applications.

Add to calendar :

Date/Time : 26 Mar 2025 17:00
Venue : S17 #04-04 (SR3)
Speaker : Chong Chi Tat, National University of Singapore

Combinatorial principles is a prominent area of investigation in reverse mathematics.

The computational complexity of a solution of an instance of a principle began with Jockusch work (1972) on Ramsey’s theorem over the standard model of Peano arithmetic. In general, every instance of a combinatorial principle has a definable solution over the standard model.

For an arbitrary model of RCA_0, however, the situation is not clear. There exist weak models and instances of combinatorial principles (such as Ramsey’s theorem for pairs) for which no definable solution is known. In this talk we present an analysis of the problem of definable solutions and some nonexistence results.

Add to calendar :

Date/Time : 26 Mar 2025 16:30
Venue : S17 #06-11 (SR6)
Speaker : Wang Chushan, National University of Singapore

The nonlinear Schrödinger equation (NLSE) arises from various applications in quantum physics and chemistry, nonlinear optics, plasma physics, Bose-Einstein Condensates, etc. In these applications, it is necessary to incorporate low-regularity or singular potential and nonlinearity into the NLSE. Typical examples of such potential and nonlinearity include the discontinuous square-well potential, the singular Coulomb potential, the non-integer power nonlinearity, and the logarithmic nonlinearity. Such low regularity and singularity pose significant challenges in the analysis of standard numerical methods and the development of accurate, efficient, and structure-preserving schemes.

In this talk, I will introduce several new analysis techniques to establish optimal error bounds for some widely used numerical methods under optimally weak regularity assumptions. Based on the analysis, we also propose novel temporal and spatial discretizations to handle the low regularity and singularity more effectively.

Add to calendar :

Date/Time : 26 Mar 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Edmund Karasiewicz, National University of Singapore

In this mini course we will study two topics. The first is the PGL2xF4 exceptional theta correspondence over a p-adic field. The second is the dual group of a spherical variety. Over the course of four lectures we will:

1. Introduce exceptional groups, focusing on constructions and tools relevant to the exceptional theta correspondence.
2. Describe the PGL2xF4 exceptional theta correspondence over a p-adic field.
3. Present the combinatorial construction of the dual group of a spherical variety due to Knop-Schalke.
4. Connect the exceptional theta correspondence to the F4/Spin9 spherical variety.

Join Zoom Meeting
https://nus-sg.zoom.us/j/84884850855?pwd=bvokLMShAf5wFeAHh2zemmel1dvb9f.1

Meeting ID: 848 8485 0855
Passcode: 226224

Add to calendar :

Date/Time : 26 Mar 2025 15:00
Venue : S17 #04-04 (SR3)
Speaker : Kim Sunghan, Uppsala University

Constraint maps are critical points to the Dirichlet energy subject to an image constraint. Namely, the constraint restricts these maps to lie outside a given (smooth, open-connected) set in the target space, which can then be thought of as an obstacle. The target space is multi-dimensional, making this problem a natural extension of the obstacle problem into the vectorial setting. The presence of the obstacle naturally induces free boundary, which is the interface between the set where the image of the maps lies away from the obstacle and the set where their image lies on the obstacle. Yet, constraint maps also develop singularities, such as discontinuous points and branch points which have been the main subjects in the theory of harmonic maps and minimal surfaces, respectively. In this talk, I will discuss the recent breakthroughs on the tantalizing interplay between the free boundary and the mapping singularities for energy-minimizing constraint maps, based on a series of my collaboration with Alessio Figalli, André Guerra (ETH), and Henrik Shahgholian (KTH).

Add to calendar :

Date/Time : 26 Mar 2025 14:00
Venue : S17 #06-11 (SR6)
Speaker : Jiuzu Hong, University of North Carolina at Chapel Hill

Global Schubert varieties of parahoric Bruhat-Tits group schemes were introduced by Xinwen Zhu in his proof of the coherence conjecture of Pappas-Rapoport. These global Schubert varieties provide flat families relating spherical Schubert varieties in affine Grassmannians and other Schubert varieties or their unions in partial affine flag varieties. In a series of talks, I will give an introduction to this topic and discuss several applications based on my own research.

In the first talk, I will cover the basics of affine Grassmannian and Schubert varieties.
In the second talk, I will discuss parahoric group schemes and flag varieties of loop groups.
In the last talk, I will introduce the global Schubert varieties of parahoric Bruhat-Titis group schemes and discuss some of their applications.

Add to calendar :

Date/Time : 25 Mar 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Jiuzu Hong, University of North Carolina at Chapel Hill

Global Schubert varieties of parahoric Bruhat-Tits group schemes were introduced by Xinwen Zhu in his proof of the coherence conjecture of Pappas-Rapoport. These global Schubert varieties provide flat families relating spherical Schubert varieties in affine Grassmannians and other Schubert varieties or their unions in partial affine flag varieties. In a series of talks, I will give an introduction to this topic and discuss several applications based on my own research.

In the first talk, I will cover the basics of affine Grassmannian and Schubert varieties.
In the second talk, I will discuss parahoric group schemes and flag varieties of loop groups.
In the last talk, I will introduce the global Schubert varieties of parahoric Bruhat-Titis group schemes and discuss some of their applications.

Add to calendar :

Date/Time : 24 Mar 2025 14:00
Venue : S17 #05-11 (SR5)
Speaker : Wei-Hsuan Yu, National Central University

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n≥6 as well as the exact size of maximal binary constant weight codes with 2,3, and 4 distances for several values of the weight and for all but small lengths.

Add to calendar :

Date/Time : 24 Mar 2025 15:00
Venue : S17 #05-11 (SR5)
Speaker : Chia-En Chiang, National Taiwan Normal University

An almost k-cover of the hypercube Q^n = {0,1}^n is a collection of hyperplanes that avoids the origin and covers every other vertex at least k times. When k is large with respect to the dimension n, Clifton and Huang asymptotically determined the minimum possible size of an almost k-cover. Central to their proof was an extension of the LYM inequality, concerning a weighted count of hyperplanes.

In this paper we completely characterise the hyperplanes of maximum weight, showing that there are $\binom{2n-1}{n}$ such hyperplanes. We further provide stability, bounding the weight of all hyperplanes that are not of maximum weight. These results allow us to effectively shrink the search space when using integer linear programming to construct small covers, and as a result we are able to determine the exact minimum size of an almost k-cover of Q^6 for most values of k. We further use the stability result to improve the Clifton–Huang lower bound for infinitely many choices of k in every sufficiently large dimension n.

Add to calendar :