Date/Time : 14 Feb 2025 11:00
Venue : S17 #05-11 (SR5)
Speaker : Benoît Corsini,

In this talk, I will present an upcoming result regarding the local evolution of Prim’s algorithm seen as a random process on graphs. To do so, I will start by introducing the concept of local limit for a sequence of graphs, before defining Prim’s algorithm and showing its relation to the minimum spanning tree. Finally, I will combine these two concepts to provide a representation of the limit, in particular its relation to invasion percolation and the percolation levels of a graph.

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Date/Time : 14 Feb 2025 15:00
Venue : S16 #03-06
Speaker : Xiong Jingang, Beijing Normal University

I will talk about the extinction dynamics of nonnegative solutions to the fast diffusion equation within bounded, smooth domains subject to the Dirichlet zero boundary condition. Initially, I will provide a concise overview of the comprehensive understanding achieved for the subcritical regime of this equation. Subsequently, I will shift my focus to the critical case, which remains an active area of investigation. Under the two-bubble energy threshold assumption on the initial data, we prove the dichotomy that every solution converges uniformly, in terms of relative error, to either a steady state or a blowing-up bubble. This is joint with Tianling Jin at HKUST.

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Date/Time : 14 Feb 2025 11:00
Venue : S17 #04-04 (SR3)
Speaker : Wang Yutong, National University of Singapore

When formalizing problems in high-school and undergraduate level, we encounters different types of formulas and equalities from time to time, and one of the most critical steps is to simplify and solve them in efficient ways. This is also the step where most beginners feel tedious and challenging. In this course, we will dive into tactics like simp, linarith, norm_num, group, ring, etc to make the process easier. If time permitted, we will also briefly explain how you can design your own tactics to provide further simplifications. Various examples and practices will be given in this course.

This mini-course will live stream. Here are the zoom ID and the link:
https://nus-sg.zoom.us/j/81322620719?pwd=Wg8FVTZbfX4QpZ7vbiYwaBN3n1MO7A.1

Meeting ID: 813 2262 0719
Passcode: 359631

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Date/Time : 14 Feb 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Luca Makowiec, National University of Singapore

We will introduce Random Spanning Trees in Random Environment (RSTRE), a disordered system on spanning trees that interpolates between the Uniform Spanning Tree (UST) and Minimum Spanning Tree (MST) measures. Our primary goal is to study how local and global observables of the RSTRE depend on the inverse temperature beta. Of particular interest is the diameter of a (typical) spanning tree, as it is the first step towards establishing convergence to a non-trivial scaling limit. Furthermore, for the RSTRE on the complete graph with uniform disorder, we discuss a sharp transition of the local limit of the RSTRE to either the UST or MST local limit. This stands in contrast to our conjectured smooth transition of the diameter when beta is inside the so-called intermediate regime.

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Date/Time : 13 Feb 2025 16:00
Venue : S17 #05-11 (SR5)
Speaker : Xiong Yunfeng, Beijing Normal University

Human behaviors have non-negligible impacts on spread of contagious disease. For instance, large-scale gathering and high mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may effectively reduce contacts and suppress the peak of the outbreak. In order to understand how spatial characteristics like population mobility and clustering interplay with epidemic outbreaks, we formulate an interacting particle system via an agent-based biased random walk model on a two-dimensional lattice. The “popularity” and “awareness” variables are taken into consideration to capture human natural and preventive behavioral factors, which are assumed to guide and bias agent movement in a combined way. Numerical study of the particle system and its continuum limit, a class of Keller-Segel PDEs with logarithm sensitivity, reveals that the spatial heterogeneity, like social influence locality and spatial clustering induced by self-aggregation, potentially suppresses the contacts between agents and consequently flats the epidemic curve. Surprisedly, disease responses might not necessarily reduce the susceptibility of informed individuals and even aggravate disease outbreak if each individual responds independently upon their awareness. The disease control is achieved effectively only if there are coordinated public-health interventions and public compliance to these measures. Our model may help evaluate a variety of public-health policies.

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Date/Time : 12 Feb 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Fukushi Kenji, Kyoto University

The extension of Morse theory to S^1 valued Morse functions, more generally, closed 1-form is called Morse-Novikov theory. Morse-Novikov theory gives a new invariants of manifolds, the Novikov homology. As in Morse homology, the essence is the trajectory of the gradient flow connecting the critical points.

Based on this, Michael Farber extended Lusternik-Schnirelmann category to closed 1-form.

Unlike the ordinary result of Lusternik-Schnirelmann category about the number of critical points of functions, this extended category no longer gives the lower bound of the number of zeros of closed 1-forms. However, if the number of zeros of closed 1-form is less than this category, the dynamics of the gradient flow of the closed 1-form must have a Homoclinic cycle.

In this talk, I will explain the Lusternik-Schnirelmann category of closed 1-form, and I will introduce the extension of the Farber’s result to non compact manifolds.

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Date/Time : 12 Feb 2025 15:00
Venue : S17 #04-04 (SR3)
Speaker : Ni Lei, University of California, San Diego

In this talk, I will review some applications of Lie theory in geometry such as Cartan’s work on symmetric spaces, Hamilton’s observation and Boehm-Wilking’s constructions utilizing Lie brackets and some highly useful considerations from Lie theory. Then I will talk about some more recent applications in my joint/solo works.

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Date/Time : 12 Feb 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Ma Jiajun, Xiamen University and Xiamen University Malaysia

This mini-course explores the fundamental aspects of local theta correspondence. The series consists of 5 lectures covering the following topics:

1. Models of the Heisenberg-Weil representation and the Metaplectic group
2. Dual pairs and general properties of theta correspondences
3. Theta correspondences over real fields
4. Theta correspondences over finite fields and p-adic fields
5. Geometric aspects of theta correspondence

This mini-course is designed for senior undergraduate students and graduate students.

This mini-course will live stream. Here is the zoom ID:
Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 12 Feb 2025 16:30
Venue : S17 #06-11 (SR6)
Speaker : Cai Yongyong, Beijing Normal University

We introduce two conservative Crank-Nicolson type finite difference schemes and a Chebyshev collocation scheme for the nonlinear Schrodinger equation with a Dirac delta potential in 1D. The key to the proposed methods is to transform the original problem into an interface problem. Different treatments on the interface conditions lead to different discrete schemes and it turns out that a simple discrete approximation of the Dirac potential coincides with one of the conservative finite difference schemes. Both Crank-Nicolson finite difference methods enjoy the second order convergence rate in time, and the first-order/second-order convergence rates in space, depending on the approximation of the interface condition. Furthermore, the Chebyshev collocation method has been established by the domain-decomposition techniques. Numerical examples are provided to support our analysis and study the orbital stability and the motion of the solitary solutions.

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