Recent Research Talks in the UTC Department of Mathematics Colloquium Series

Since 1999, the department has sponsored the Colloquium Series. This provides both UTC math faculty as well as guest speakers the opportunity to highlight their most recent research in the field of mathematics.

Fall 2025

Vladimir Vladicic

• Date/Time: Fri., Sept. 5 at 2:30PM
• Location: Lupton 393
• Title: Inverse spectral problems: From Ambarzumian’s theorem to theorem of uniqueness
• Abstract: Inverse spectral theory its roots back to classical results such as Borg’s two spectra theorem and Ambarzumian’s theorem, which provide foundational insights into how the spectrum of a Sturm-Liouville operators determines its potential.
  In his famous paper ”Uber eine Frage der Eigenwerttheeorie” from (1929) Ambarzumian describes the exceptional case in wich the spectrum of boundary value problem generated with Sturm-Liouville operator under Neumann boundary conditions uniquely determines potential. In general, the specification of the spectrum does not uniquely determined potential. 
  Borg(1946) proved Theorem of uniqueness from two spectra of the boundary value problem defined with Sturm-Liouville operator under Robin boundary conditions. 
  In addition to this result, many mathematicians contributed to the determination potential functions or proved the uniqueness of the potential based on other spectral characteristics like spectral function, spectral data or Weyl function and we can say that inverse problem for Sturm-Liouville differential operators is fully solved.
  One of the most important direction for further research was BVPs generated with a Sturm-Liouville type differential equation with a constant delay and one of the first resulat was given by Freiling and Yurko (2012) and they proved Ambarzumian type theorem for differential operators defined with Sturm-Liouville equation with constant delay under Dirichlet-Neumann boundary conditions from two spectra. Compared with Ambarzumian’s theorem it could be expected that Borg-type inverse problem for this BVP will be more complicated than in the case of classical Sturm-Liouville operator. In several papers authors solve Borg-type inverse spectral problems for this class of the boundary value problems and they give complete answer for which value of the delay Theorem of uniqueness from two spectra is true or not true.
  There has recently been increasing interest in boundary value problems generated by Sturm–Liouville operators with more than one constant delay. In the case with two constant delays an attempt was made to answer the question of how many spectra are needed for Ambarzumian’s theorem to be correct, but until now we don’t have answer. Also, we don’t have complete
  answer when potential function is unique ordered.
  The focus of this research is on the boundary value problems generated with differential equation Sturm-Liouville-type two constant delay. The Ambarzumian type theorem for operator with two constant delays from four spectra will be proven and a partial answer to the question of when the Theorem of uniqueness is true and when it is not will be given.

Ayca Cetinkaya

• Date/Time: Fri., Sept. 12 at 2:30 p.m.
• Location: Lupton 393
• Title: From difference to differential equations: Eigenvalue problems via Prufer transformation
• Abstract: In this talk, I will present a parallel approach for eigenvalue problems in both discrete and continuous settings. Starting from second-order difference equations and then moving to second-order differential equations, I will show how the Pr¨ufer transformation translates these problems into systems of first-order linear equations. This transformation not only reveals the underlying structure but also provides a natural framework for both analytical insights and numerical techniques for eigenvalue estimation.

Ziwei Ma

• Date/Time: Fri., Sept. 19 at 3:20 p.m.
• Location: Lupton 393
• Title: Some work on "wrong skewness" problem in stochastic frontier model
• Abstract: The stochastic frontier model (SFM) is an econometric approach used to estimate production or cost efficiency by separating random noise from inefficiency in observed output. The main idea of SFM is to distinguish between random shocks and systematic inefficiency, which makes SFM is one of the most powerful tools for efficiency analysis. While like most other models, it has limitations, like being sensitive to the distributional assumptions and bias efficiency estimates by misspecification of the production function. But the "wrong skewness" problem will lead to the whole result being invalid. In this talk, some recent work on handling the "wrong skewness" problem will be presented, including generalized models of random noise, estimation algorithm improvement. In the end, several further directions of further improvement will be discussed.

Thien Le

• Date/Time: Fri., Oct. 3 at 3:20 p.m.
• Location: Lupton 393
• Title: Universally consistent tests for the graph of a Gaussian graphical model
• Abstract: The Gaussian graphical model is widely used to capture the joint distribution of multiple random variables, with its induced graph offering both interpretability and improved estimation efficiency. They play a central role in applications such as inferring gene networks in genomics, mapping brain connectivity in neuroscience, and modeling dependencies among financial assets. Although estimation methods are well developed, tests for whether a proposed graph is adequate remain limited. This talk introduces new goodness-of-fit tests that are computationally simple yet theoretically rigorous. We propose a simple plug-in test and an enhanced version that achieves universal consistency, both following a Gumbel distribution under the null. Simulations confirm the procedures have the correct size under the null and strong power under alternatives. An application to COVID-19 data illustrates their value in selecting graph structures for efficient estimation.

Spring 2026

Coming Soon

• Date/Time:
• Location:
• Title:
• Abstract: