DUKE NCCU NC State UNC
| 9:30 - 10:00 am EDT | Welcome Coffee |
| 10:00 - 10:15 am EDT |
Welcoming Remarks
SAS 2203 Lewis Owen, Dean, College of Sciences, North Carolina State University SAS 2203 Alina Chertock, Head, Department of Mathematics, North Carolina State University |
| 10:15 - 11:05 am EDT |
Digital Twins, Generative AI, and Beyond: A PDE–Constrained Optimization Perspective
SAS 2203 Speaker Harbir Antil, George Mason University Session Chair Hien Tran, North Carolina State University Abstract Digital Twins (DTs) are adaptive, real-time virtual replicas of physical systems that integrate physics-based models, sensor data, and intelligent decision-making. At their core, DTs can be rigorously framed within PDE–constrained optimization (PDECO). This talk develops a unified PDECO framework for state estimation and control, leveraging adjoint-based methods in both deterministic and stochastic settings. To address the challenges of infinite-dimensional, large-scale optimization, we introduce novel function-space trust-region and augmented Lagrangian algorithms, and explore the role of randomized methods in dynamic PDECO. A central theme is a new connection between PDECO and Generative AI: score-based generative models can be interpreted as backward-in-time PDEs, linking ill-posed inverse problems, stability analysis, and modern machine learning. This perspective bridges physics-informed modeling with data-driven synthesis, opening the door to, for instance, score-based Digital Twins. Applications span a wide range of domains, including structural and biomedical systems—from bridges and dams to aneurysm modeling, optimal insulation, electromagnetic cloaking, light bending, fusion, and neuromorphic computing. Together, these examples highlight a pathway toward predictive, adaptive, and trustworthy Digital Twins and AI technologies. |
| 11:10 am - 12:00 pm EDT |
Detection of Cancer Chromosome Aberrations via Topological Data Analysis and Graph-Theoretic Methods
SAS 2203 Speaker Radmila Sazdanovic, North Carolina State University Session Chair Semyon Tsynkov, North Carolina State University Abstract Chromosome instability and structural aberrations are hallmarks of cancer, with copy number aberrations (CNAs), amplifications and deletions of genomic regions, playing a central role in tumor progression. Among these, driver aberrations affecting proto-oncogenes or tumor suppressor genes are particularly difficult to detect because of noise and overlapping signals from passenger CNAs. This talk first introduces Topological Analysis of array CGH (TAaCGH), a topology-based method developed by Arsuaga et al. that maps copy number changes to specific cancer phenotypes, with applications to breast cancer. We then present a graph-theoretic framework for reconstructing cancer chromosome exchange pathways, enabling robust inference even with missing or low-resolution data. This approach extends previous work in radiation biology and evolutionary genomics, offering new tools for understanding the complex genomic rearrangements driving cancer progression. This is joint work with Javier Arsuaga and his lab at UC Davis, and S. Sheth at NC State. |
| 12:00 - 1:30 pm EDT |
Lunch/Free Time
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| 1:30 - 2:20 pm EDT |
KPZ growth, interfaces, and shocks
SAS 2203 Speaker Alexander Dunlap, Duke University Session Chair Hongkai Zhao, Duke University Abstract The KPZ equation is a Hamilton-Jacobi equation with random forcing that models the growth of a random surface. It is a prototypical member of the KPZ universality class, which is a large class of probabilistic models exhibiting non-Gaussian statistics at large scales. I will give a gentle introduction to these objects and the mathematics surrounding them. Then I will mention some connections with shock solutions to the viscous Burgers equation (based on some joint works with Lenya Ryzhik and Evan Sorensen). |
| 2:25 - 2:55 pm EDT |
Coffee Break
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| 3:00 - 4:30 pm EDT |
Lightning Session
SAS 2203 Speakers Yuliang Wang, Duke University Ala' Alalabi, North Carolina State University Vasishta Tumuluri, University of North Carolina - Chapel Hill Aaron Jacobson, University of North Carolina - Chapel Hill Harshit Bhatt, North Carolina State University Avery Paulsen, North Carolina State University Pat Haughey, North Carolina State University Ryan Rinaudo, North Carolina State University Matthew Nuyten, North Carolina State University Aric Wheeler, Duke University Thuy Le, North Carolina State University Julia Sanger, North Carolina State University Bryan Castillo, Duke University Zihao Yu, North Carolina State University Amartya Banerjee, University of North Carolina - Chapel Hill Frane Ljubetic, University of North Carolina - Chapel Hill Nakul Haridas, North Carolina State University Patrick Martin II, North Carolina State University Troy Larsen, North Carolina State University Paul Spears, North Carolina State University Minji Kim, University of North Carolina - Chapel Hill Ford Khoudary, University of North Carolina - Chapel Hill David Hernandez, North Carolina State University Alexander Richardson, North Carolina State University Shenghan Mei, University of North Carolina - Chapel Hill Perry Beamer, North Carolina State University Session Chair Hien Tran, North Carolina State University |
| 4:30 - 5:30 pm EDT |
Panel Discussion on Opportunities for Faculty, Postdocs, and Graduate Students
SAS 1102 Panelists Kidist Maxwell, Applied Research Associates (ARA) Richard Allen, Pfizer Philip Warrick, PeriGen Moderators Greg Forest, University of North Carolina - Chapel Hill Mansoor Haider, North Carolina State University |
| 5:30 - 7:30 pm EDT |
Social and Poster Session SAS 2nd Floor Atrium Poster Presenters Zihao Yu, North Carolina State University Elly Do, North Carolina State University Troy Larsen, North Carolina State University Julia Sanger, North Carolina State University Jessie Chen, North Carolina State University Sam Thornton, North Carolina State University Madhumita Roy, North Carolina State University Harshit Bhatt, North Carolina State University Patrick Martin II, North Carolina State University Paul Spears, North Carolina State University Matthew Nuyten, North Carolina State University Nakul Haridas, North Carolina State University Pat Haughey, North Carolina State University Ala' Alalabi, North Carolina State University Chuxiangbo Wang, University of North Carolina - Chapel Hill Ian Stevenson, University of North Carolina - Chapel Hill Kaitlyn Hohmeier, University of North Carolina - Chapel Hill Amartya Banerjee, University of North Carolina - Chapel Hill Yi Gong, University of North Carolina - Chapel Hill David Hernandez, North Carolina State University Aric Wheeler, Duke University Jiaqi Zhang, Duke University Ling Zhou, Duke University Lorenzo Micalizzi, North Carolina State University Yuliang Wang, Duke University Chenxi (Thea) Wang, University of North Carolina - Chapel Hill Kangning Cui (Jason), Wake Forest University Shenghan Mei, University of North Carolina - Chapel Hill Connor Magoon, University of North Carolina - Chapel Hill Frane Ljubetic, University of North Carolina - Chapel Hill Xinyun Liu, University of North Carolina - Chapel Hill John Albright, University of North Carolina - Chapel Hill Vasishta Tumuluri, University of North Carolina - Chapel Hill Thuy Le, North Carolina State University Avery Zapata, University of North Carolina - Chapel Hill Alexander Richardson, North Carolina State University Bryan Castillo, Duke University Nabiha Choudhury, University of North Carolina - Chapel Hill Philip Warrick, PeriGen Canada; McGill University Klaas van de Groep, University of North Carolina - Chapel Hill Justin Hager, University of North Carolina - Chapel Hill Ford Khoudary, University of North Carolina - Chapel Hill Madhusudan Madhavan, North Carolina State University Perry Beamer, North Carolina State University Aaron Jacobson, University of North Carolina - Chapel Hill Avery Paulsen, North Carolina State University Joseph Clampett, University of North Carolina - Chapel Hill Minji Kim, University of North Carolina - Chapel Hill Chuying Huo, Duke University Meghan Kwon, Duke University Ryan Rinaudo, North Carolina State University See all Abstracts Here! |
| 9:00 - 9:30 am EDT | Welcome Coffee |
| 9:30 - 10:20 am EDT |
Walking droplets & Galloping bubbles
SAS 2203 Speaker Pedro Saenz, University of North Carolina - Chapel Hill Session Chair Greg Forest, University of North Carolina - Chapel Hill Abstract Through a combination of experiments, simulations, and theory, we will discuss two problems that exemplify the research carried out in UNC’s Physical Mathematics Laboratory, each motivated by fundamental questions in physics and engineering. In the first part, we present a classical wave–particle analog of Anderson localization using walking droplets, or “walkers”, which self-propel across a vibrating fluid bath via a resonant interaction with their own guiding wave field. These droplets push the boundaries of classical mechanics by exhibiting behaviors once thought to be exclusive to the quantum realm. By investigating the erratic motion of walkers over submerged random topographies, we demonstrate the emergence of localized statistics analogous to those observed in quantum particles. Analysis of walker trajectories reveals a suppression of diffusion when the guiding wave field extends over the disordered topography, an effect driven by a wave-mediated resonant coupling with the topography that gives rise to an confining wave potential. This hydrodynamic quantum analog illustrates how a classical particle may localize like a wave. In the second part, we introduce a new symmetry-breaking mechanism that enables bubbles to “gallop” along horizontal surfaces in a vertically vibrated fluid chamber, propelled by a coupling between shape oscillation modes. The resulting active bubbles exhibit a variety of trajectory regimes (rectilinear, orbital, and run-and-tumble) that can be tuned by external forcing parameters. Harnessing periodic body deformations and inertial forces, galloping bubbles achieve self-propulsion without net external forcing along their direction of motion. Proof-of-concept demonstrations illustrate the potential of this galloping motion for applications in bubble manipulation, transport, and sorting, navigation through complex fluid networks, and surface cleaning. |
| 10:30 - 11:20 am EDT |
Highlights of exciting research at NC State Mathematics Department
SAS 2203 Speakers Hangjie Ji: Optimal control of droplet dynamics Xiao Shen: Random growth in the KPZ universality class Arvind Saibaba: Randomized numerical linear algebra Bojko Bakalov: Lie algebras and quantum machine learning Zixuan Cang: Optimal transport for mapping cells across space, time, and modality Fatma Terzioglu: Mathematical methods for tomographic image reconstruction Erik Bates: Avoidance Couplings: random walkers who agree to disagree Chao Chen: Fast Matrix Computations for Scientific Computing Session Chair Alina Chertock, North Carolina State University |
| 11:30 am - 1:00 pm EDT |
Lunch (provided by organizers)
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| 1:00 pm EDT | Conference Adjourn |