NYCU Applied Mathematics Colloquium are held every Tuesday 2-3 pm. Place: SA223
Organizer: Yi-Hsuan Lin
Invited Speakers
Date: September 12, 2023, 2:00pm-3:00pm.
Take your students ID cards.
Date: September 19, 2023, 2:00pm-3:00pm.
Speaker: Prof. Cătălin I. Cârstea. Department of Applied Mathematics, National Yang Ming Chiao Tung University.
Title: A density property for tensor products of gradients of harmonic functions
Abstract: In this talk I will present a recent result showing that linear combinations of tensor products of k gradients of harmonic functions, with k at least three, are dense in C_0^infty(\Omega),
for any bounded domain \Omega in dimension 3 or higher. This kind of density result has
applications to inverse problems for elliptic quasilinear equations/systems in divergence
form, where the nonlinear part of the ”conductivity” is anisotropic.
Date: September 26, 2023, 2:00pm-3:00pm.
No Talk. Teacher's Day of Taiwan.
Date: October 3, 2023, 1:20pm-3:00pm.
Speaker: 謝欣格諮商心理師（若竹心理諮商所）
Title: 練愛的發現∼談如何養成追愛的好體質
Date: October 10, 2023, 2:00pm-3:00pm.
No talk. National Day of Taiwan.
Date: October 17, 2023, 2:00pm-3:00pm.
No Talk Today. The talk is rescheduled to January 12, 2024.
Date: October 24, 2023, 2:00pm-3:00pm.
Speaker: Prof. Chih-Hung Chang (張志鴻教授), Department of Applied Mathematics, National University of Kaohsiung.
Title: Bohr chaoticity of number-conserving shifts
Abstract: Let X be a.compact metric space and T : X → X be a continuous transformation. A dynamical system (X, T) is called Bohr chaotic if for each weight sequence (wn) ∈ l∞(N,R) there are f ∈ C(X) and x ∈ X such that (wn) is orthogonal to {f ◦Tn(x)}. In this talk, we introduce the number-conserving shifts and show that a number-conserving shift is either finite or Bohr chaotic. Furthermore, a number-conserving shift is consisting of periodic points whenever it is finite.
Date: October 31, 2023, 2:00pm-3:00pm.
Mideterm week (October 30 - November 3, 2023) break.
Date: November 7, 2023, 2:00pm-3:00pm.
No talk due to PhD entrance exam.
Date: November 14, 2023, 2:00pm-3:00pm.
Speaker: Prof. Yen-Huan Li (李彥寰教授). Department of Computer Science & Information Engineering, National Taiwan University.
Title: From universal coding to learning quantum states
Abstract: This talk will cover three closely related problems: universal coding for data compression, online portfolio selection for long-term investment, and online learning of quantum states for quantum state tomography. While the application scenarios appear distinct, these problems share similar mathematical structures. I will offer a brief introduction to all three problems and delve into state-of-the-art results for the latter two.
Date: November 21, 2023, 2:00pm-3:00pm.
Speaker: Prof. Chun-Yen Shen (沈俊嚴教授). Department of Mathematics, National Taiwan University.
Title: Discretized Sum-Product and Geometric Measure Theory
Abstract: In this talk, I will first briefly review the history of sum-product estimates in the setting of finite
fields and mention the applications of sum-product type problems. Then I will start introducing
the celebrated result of Bourgain about the discretized sum-product estimates and the applications
to geometric measure theory problems. Finally I will talk about our recent results about expanding
polynomials in continuous setting and discuss their sum-product phenomena.
Date: November 28, 2023, 2:00pm-3:00pm.
Speaker: Prof. Ying-Chung Jimmy Lin (林盈仲教授). Institute of Plant Biology, National Taiwan University.
Title: Single-cell transcriptomics unveils xylem cell development and evolution
Abstract: As the most abundant tissue on Earth, xylem is responsible for lateral growth in plants. Typical xylem has a radial system composed of ray parenchyma cells and an axial system of fusiform cells. In most angiosperms, fusiform cells are a combination of vessel elements for water transportation and libriform fibers for mechanical support, while both functions are performed together by tracheids in other vascular plants. However, little is known about the developmental programs and evolutionary relationships of these xylem cell types. Through both single-cell and laser-capture microdissection transcriptomic profiling, here we demonstrate the developmental lineages of ray and fusiform cells in stem-differentiating xylem across four divergent woody angiosperms. Cross-species analyses of single-cell trajectories reveal highly conserved ray, yet variable fusiform, lineages across angiosperms. Core eudicots Populus trichocarpa and Eucalyptus grandis share nearly identical fusiform lineages. The tracheids in the basal eudicot Trochodendron aralioides, an evolutionarily reversed character, exhibit strong transcriptomic similarity to vessel elements but not libriform fibers, suggesting that water transportation, instead of mechanical support, is the major feature. We also found that the more basal angiosperm Liriodendron chinense has a fusiform lineage distinct from that in core eudicots. This evo-developmental framework provides a comprehensive understanding of the formation of xylem cell lineages across multiple plant species spanning over a hundred million years of evolutionary history. Within the past one and half years, four research groups have published their studies in the top 5% journals on elucidating stem-differentiating xylem development. Yet, these four articles led to four conflicting models. In an attempt to sort out this puzzle, we reached out to the other corresponding authors to determine the current most plausible model.
Date: December 5, 2023, 2:00pm-3:00pm.
Speaker: Dr. Buo-Fu Chen (陳柏孚博士). Center for Weather and Climate Disaster Research, National Taiwan University.
Title: Meteorological AI Applications – From Typhoon Analysis to Pangu weather - From Regression to Modeling the System
Abstract: This presentation introduces the AI-meteorological applications developed in NTU in recent years.
The first part showcases the usefulness of deep learning (DL) for reconstructing homogenized and trustworthy global tropical cyclone (TC) wind profile datasets since 1981 and thus facilitating an examination of climate trends of TC structure/energy extremes. Understanding past TC trends and variability is critical for projecting future TC impacts on human society considering the changing climate. By training with uniquely labeled data integrating best tracks and numerical model analysis, our model converts multichannel satellite imagery to a 0-750-km wind profile of axisymmetric surface winds. The model performance is verified to be sufficient for climate studies by comparing it to independent satellite-radar surface winds. Based on the new homogenized dataset, the major TC proportion has increased by ~13% in the past four decades. Moreover, the proportion of extremely high-energy TCs has increased by ~25%, along with an increasing trend (> one standard deviation of the 40-y variability) of the mean total energy of high-energy TCs. Although the warming ocean favors TC intensification, the TC track migration to higher latitudes and altered environments further affect TC structure and energy.
In the second half of this talk, we will review a recent and impactful paper published in Nature: the Pangu-Weather. This framework swtich from the deep-learning regression tasks to modeling the entire atmospheric circulation system with data-driven AI. Our preliminary tests of this new approach for weather prediction is also carried out. Subsequently, we discuss new opportunities and plans for integrating the above DL analysis/forecasting techniques into a full data-driven mesoscale weather prediction model
Date: December 12, 2023, 2:00pm-3:00pm.
Speaker: Prof. Sheng-Hsuan Lin (林聖軒教授). Institute of Statistics, National Yang Ming Chiao Tung University.
Speaker: Prof. Sun-Yung Alice Chang (張聖容院士). Department of Mathematics, Princeton University.
Title: Conformal Geometry on 4-manifolds
Abstract: In this talk, I will give a survey talk on results and PDE techniques in conformal geometry.
On 4-manifolds, one of the key ingredients is the study of the integrand of the Chern- Gauss-Bonnet formula. The part that involves the Ricci tensor gives a fully non-linear PDE known as the second elementary symmetric equation. It turns out this PDE can be studied via a 4-th order linear operator (part of the family of GJMS operator) and its associated 4-th order curvature called the Q-curvature. I will explain the connection and give an application of using this concept to compute the renormalized volume.
As another application, we will study the problem of ”conformal filling in” in ADS/CFT
theory. Namely, given a manifold (Mn;[h]), when is it the boundary of a conformally com-
pact Einstein manifold ( Xn+1;g+) with r2 |M = h for some defining function r on Xn+1? g+
The model example is the n-sphere as the conformal infinity of the hyperbolic (n+1) ball.
Date: December 19, 2023, 2:00 pm - 3:00 pm.
Speaker: Prof. Chih-Wei Chen (陳志偉教授). Department of Applied Mathematics, National Sun Yat-sen University.
Title: Convergence of Hessian estimator from random samples on a manifold
Abstract: We provide a systematic convergence analysis of the Hessian operator estimator from random samples supported on a low dimensional manifold. We show that the impact of the nonuniform sampling and the curvature on the widely applied Hessian operator estimator is asymptotically negligible. This is joint work with Hau-Tieng Wu (Courant Institute of Mathematical Sciences, NYU).
Date: December 26, 2023, 2:00pm -3:00pm.
Speaker: Prof. Michael Melgaard (Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex).
Title: Tour of Spectral and Scattering Theory: Eigenvalues, Resonances, and Numerics
Abstract: I give an introduction to the main questions addressed in spectral and scattering theory for differential operators arising in quantum physics (e.g., with magnetic fields, relativistic effects), sprinkled with numerous examples, including Egorov’s theorem, localization of essential spectrum, eigenvalue asymptotics and resonances, phase space bounds, and modern numerical tensor methods.
Date: January 12, 2024, 11:00am - 12:00pm.
Speaker: Prof. Tin-Yau Tam (譚天祐教授). Department of Mathematics and Statistics, University of Nevada, Reno.
Title: Extensions of Yamamoto-Nayak’s asymptotic theorem
Abstract: A very recent result of Nayak asserts that limm→∞ |Am|1/m exists for each n × n complex matrix A, where |A| = (A∗A)1/2, and the limit is given in the language of linear transformation. This is an extension of Yamamoto’s result in 1967. We extend the result of Nayak, namely, we prove that limm→∞ |BAmC|1/m exists for any n × n complex matrices A, B, and C; the limit is given in matrix language and is independent of B. We then provide extensions in the context of real semisimple Lie groups.