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Posted December 27, 2025
Last modified April 11, 2026

Control and Optimization Seminar Questions or comments?

Aris Daniilidis, Technische Universität Wien
Variational Stability of Alternating Projections

The alternate projection method is a classical approach to deal with the convex feasibility problem. We shall first show that given two nonempty closed convex sets $A$ and $B$, the consecutive projections $x_{n+1} = P_B(P_A(x_n))$, $n \ge 1$ produce a self-contacted sequence, providing in particular an alternative way to establish convergence in the finite dimensional case [2]. In infinite dimensions, a regularity condition is required to ensure convergence of the above sequence $\{x_n\}_{n\ge 1}$ [4]. In [3], it was established that a regularity condition from [1] also ensures the variational stability of the above method. In this talk, we shall complete this result and show that variational stability is actually equivalent to the aforementioned regularity assumption. REFERENCES: [1] H. Bauschke, J. Borwein, On the convergence of von Neumann’s alternating projection algorithm for two sets, Set-Valued Anal. 1 (1993), 185–212. [2] A. Bohm, A. Daniilidis, Ubiquitous algorithms in convex optimization generate self-contracted sequences, J. Convex Anal. 29 (2022) 119–128. [3] C. De Bernardi, E. Miglierina, A variational approach to the alternating projections method, J. Global Optim. 81 (2021), 323-350. [4] H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. 57 (2004), 35–61.

Posted April 11, 2026

LSU AWM Student Chapter LSU AWM Student Chapter Website

AWM Officer Elections

AWM will be holding our annual officer elections for the academic year 2026-27. Any present LSU AWM member will be able to vote, with membership sign-up available day-of. Register to run with our officer candidate form. We're excited to meet the candidates! All are welcome! Don't hesitate to reach out if you have any questions.

Event contact: jgarc86@lsu.edu

Posted April 13, 2026

Combinatorics Seminar Questions or comments?

Gyaneshwar Agrahari, LSU
Counting $K_{1,t}$ and $K_{2,t}$ in higher connected triangulations

In 1979, Hakimi and Schmeichel initiated the study of the maximum number of copies of a fixed subgraph in planar graphs by determining the maximum number of \( C_3 \) and \( C_4 \) in an \( n \)-vertex planar graph. In 1984, Alon and Caro determined the maximum numbers of copies of $K_{1,t}$ and $K_{2,t}$ in an $n$-vertex planar triangulation. Throughout the years, graph theorists have solved similar problems for longer cycles, including Hamiltonian cycles, paths, and other subgraphs. In the case of Hamiltonian cycles, there are at least quadratically many Hamiltonian cycles in a 4-connected planar triangulation. However, in a 5-connected $n$-vertex planar triangulation, there are exponentially many Hamiltonian cycles, proving that connectivity can play a significant role in enumerating certain subgraphs. We determine the exact maximum number of copies of $K_{1,t}$ and $K_{2,t} $ in a $4$-connected planar triangulation, and that of $K_{1,t}$ in a $5$-connected planar triangulation. We also characterize all extremal graphs that attain these bounds.

Posted April 8, 2026

Informal Analysis Seminar Questions or comments?

Christopher Bunting, LSU
Tbd

Tbd

Posted January 15, 2026
Last modified January 22, 2026

Informal Geometry and Topology Seminar Questions or comments?

Fabian Espinoza de Osambela, Louisiana State University
TBD

TBD