I am a mathematician by training, with broad interests in how combinatorial structure helps us understand complex systems and makes computationally difficult problems tractable.
Much of my work is to seek meaningful combinatorial structure such that the optimization problem on top of it becomes easy. It centers on understanding how graph structure determines the optimization landscape of synchronization problems, using tools from combinatorics, graph theory, low-rank semidefinite optimization, and dynamical systems. I'm also interested in developing a theoretical understanding of collective behavior that emerges in natural and social systems, as well as system resilience and robustness. See what I caught on Pi Day in Rapperswil.
Publications & preprints
Synchronization & nonconvex optimization
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Benign nonconvexity of synchronization landscapes induced by graph skeletons
Submitted · arXiv:2512.21935
Research summary
We study the homogeneous Kuramoto model on a graph and the associated nonconvex optimization problem . The objective defines an energy over configurations of points on the unit circle and serves as a Lyapunov potential for the dynamics. We prove that every connected quasi-threshold graph is second-order globally synchronizing: every second-order stationary point is a global minimizer corresponding to full synchronization. Consequently, the dynamics converge to full synchronization from almost every initial condition. These graphs are precisely the comparability graphs of partially ordered sets induced by rooted trees. Viewing these trees as graph skeletons, we establish an upward propagation mechanism: synchronization within each child subtree forces the parent and all its descendants to synchronize. The argument proceeds from the leaves to the root and relies on phasor geometry and second-order optimality conditions. Our result provides a structural route to global synchronization that complements existing results based on minimum-degree or spectral proximity to complete graphs.
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Global synchronization beyond dense graphs: the case of threshold graphs
Submitted · arXiv:2511.12646
Research summary
Given a graph G with adjacency matrix A, consider the homogeneous Kuramoto energy . We call G second-order globally synchronizing if every second-order stationary point of EG is fully synchronized. This property implies global synchronization, namely that, up to a measure-zero set of initial conditions, trajectories of the Kuramoto model converge to a fully synchronized state. A fundamental graph-theoretic question is to identify which graph structures have this property. Existing guarantees for global synchronization typically require large minimum degree which forces the graph to be very dense, or good expansion properties. In this paper, we show that synchronization can also arise from a different, purely structural mechanism. More precisely, we prove that threshold graphs, a classical recursively defined graph class, are second-order globally synchronizing, and hence globally synchronizing. Thus, globally synchronizing graphs need not be very dense, have large minimum degree, or satisfy strong expansion-type conditions. The proof exploits the recursive construction of threshold graphs: local phasor constraints imposed by second-order stationarity are propagated along the construction sequence until full synchronization is forced.
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Global synchronization of inductively defined graph classes: a local-to-global perspective
PhD Thesis · ETH Zürich
Analysis & partial differential equations
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Global boundedness of the curl for a p-curl system in convex domains
Mathematical Methods in the Applied Sciences
Visualization
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VisAct: a visualization design system based on semantic actions
Journal of Visualization
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Task-oriented optimal sequencing of visualization charts
IEEE Symposium on Visualization in Data Science
Presentations & experience
Selected presentations
Threshold graphs are globally synchronizing
The 6th EUROYoung workshop, Lugano, Switzerland, October 2026.
Global synchronization beyond dense Graphs: the case of threshold graphs
FoCM 2026, Combinatorics and graph theory session, Vienna, Austria, July 2026.
PosterSkeleton of globally synchronizing graphs
Talk at the Mittagsseminar, Theory of Combinatorial Algorithms, ETH Zurich, November 2025.
SlidesBenign nonconvexity and global synchronization with nonlinear interactions
Workshop “Algorithmic Optimization: Tools for AI and Data Science” (50 Years of Yurii Nesterov’s Research), August 2024.
Global boundedness of the curl for a p-curl system in convex domains
Talk at Tsinghua University, March 2019.
Empirical research
Use of network models of epidemic spread and in particular SARS-CoV-2
LinkSignificant dynamic graphlets mining for clinical phenotype analysis in brain injury data
Link
Industrial/practical experience
Intern @Tencent CSIG Jarvis Lab
build a data visualization platform for monitoring anomalies in large-scale internal computing systems.
Research Intern @ Chair of Systems Design, ETH Zurich
- Topic: Link Prediction and Construction in Temporal Multilayer Networks
- Project report: Genua Analysis
- Advisors: Prof. Frank Schweitzer, Christoph Gote, Christian Zingg
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