AG meets ML

Aim and Scope: We bring researchers in algebraic geometry together to discuss their research projects, exchange ideas, and explore possible work related to machine learning.  

Time: 4/29 10:00-11:30 am, 2:30-4:00 pm

Venue: 301 Conference Room

         Department of Math, National Cheng Kung University

Invited Speaker 

Pedro Núñez (NTU)       

Jason Lo (CSUN)

Flora Poon (NCTS)  

Tsung-Ju Lee (NCKU)

Sam Wang (Utah)   

Ching-Jui Lai (NCKU)

Schedule

4/28   13:00 ~ 17:00 Warmup discussion

4/29   10:00 ~ 11:30 20-min Short talks + 5 min QA

Jason Lo, CSUN

Title: From data to concepts via wiring diagrams

Abstract: The idea of ologs was invented by Spivak around 10 years ago, and provides a method for organizing data and concepts using elementary category theory.  In this talk, I will introduce the idea of wiring diagrams as an extension of ologs, and discuss our work in progress on extracting wiring diagrams from COVID patient data.  No algebraic geometry is required for this talk.

Ching-Jui Lai, NCKU

Title: Fano manifolds with unstable tangent bundles

Abstract: We describe our project of revealing the geometry of unstable Fano manifolds, our first result on the complete classification in dimension two, and difficulties in extending this program to higher dimensions. 

Flora Poon, NCTS 

Title: Brauer twists of K3 surfaces admitting van Geemen-Sarti involution 

Abstract: For any lattice polarised elliptic K3 surface, van Geemen's Brauer twist construction associates to any order 2 element in its Brauer group another elliptic K3 surface, where the original K3 surface can be recovered by taking the relative Jacobian fibration. We will give explicit geometric constructions of some of the Brauer twists of a very general K3 surface that admits a van Geemen-Sarti involution, as well as their birational models. This is an ongoing work with Adrian Clingher and Andreas Malmendier.

11:30 ~ 12:50 Lunch

14:30 ~ 16:00 20-min Short talk + 5 min QA

Pedro Núñez, NTU

Title: Derived categories of hyperelliptic varieties

Abstract: Hyperelliptic varieties are smooth projective varieties which are quotients of abelian varieties by finite groups acting freely and not only via translations. In this talk, we discuss the indecomposability of derived categories of hyperelliptic threefolds, which is a consequence of a structure theorem for their Albanese morphism. We also discuss some open problems related to derived categories of hyperelliptic varieties. This is joint work with Pieter Belmans and Andreas Demleitner.

Shih-Hsin (Sam) Wang, Utah

Title: A Theoretically-Principled Sparse, Connected, and Rigid Graph Representation of Molecules

Abstract: Graph neural networks (GNNs) -- learn graph representations by exploiting graph's sparsity, connectivity, and symmetries -- have become indispensable for learning geometric data like molecules. However, the most used graphs (e.g., radial cutoff graphs) in molecular modeling lack theoretical guarantees for achieving connectivity and sparsity simultaneously, which are essential for the performance and scalability of GNNs. Furthermore, existing widely used graph construction methods for molecules lack rigidity, limiting GNNs' ability to exploit graph nodes' spatial arrangement. In this paper, we introduce a new hyperparameter-free graph construction of molecules and beyond with sparsity, connectivity, and rigidity guarantees. Remarkably, our method consistently generates connected and sparse graphs with the edge-to-node ratio being bounded above by 3. Our graphs' rigidity guarantees that edge distances and dihedral angles are sufficient to uniquely determine the general spatial arrangements of atoms. We substantiate the effectiveness and efficiency of our proposed graphs in various molecular modeling benchmarks. Code is available at \url{https://github.com/Utah-Math-Data-Science/UnitSphere}.

Tsung-Ju Lee, NCKU

Title: Non-Kahler CY’s and their moduli 

Abstract: In this talk, we will discuss various metrics on the moduli spaces of non-Kahler CY 3-folds and their properties.

4/30  9:00 ~ 12:00  Open discussion 

            Afternoon: Excursion