Time & Location: All talks are on Thursdays in TBA at 3:30 pm unless otherwise noted. Refreshments in Gibson 426 after the talk.
Organizer: Tommaso Buvoli and Samuel Punshon-Smith
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***Tuesday, January 20,***
Special Colloquium
Title: Evolution equations in physical and biological systems
Speaker: Selim Sukhtaiev - Auburn University
Abstract: Disorder and pattern formation are central themes in modern science, and both play a fundamental role in the behavior of complex physical and biological systems. In this talk, we will discuss two mathematical models that illustrate these phenomena: the Anderson model of electronic transport in random media and the Keller–Segel model of chemotaxis.
We will first turn to a mathematical treatment of the Anderson model. We will discuss several natural Hamiltonians on metric trees with random branching numbers and show that their transport properties are suppressed by disorder. This phenomenon, known as Anderson localization, is a hallmark of the spectral theory of Schrodinger operators.
We will then consider the Keller–Segel system, a coupled pair of reaction–advection–diffusion equations describing the collective motion of cells in response to chemical signals. We will focus on well-posedness of this system on arbitrary compact networks, as well as the asymptotic stability, instability, and bifurcation of steady states in both the parabolic–parabolic and parabolic–elliptic realizations of the Keller–Segel model.
Location: Dinwiddie 108
Time: 3:30PM
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***Thursday, January 22,***
Special Colloquium
Title: Large Effects in Perturbed Hamiltonian Systems
Speaker: Marian Gidea - Yeshiva University
Abstract: One of the fundamental laws of physics is the conservation of energy, which states that the total energy of an isolated system remains constant.
Hamiltonian dynamics provides a natural framework for modeling this law. However, real-life systems are rarely isolated and are subject to external perturbations of various types, such as periodic / quasi-periodic forcing, random perturbations, or dissipation. In this lecture, we will consider several models from celestial mechanics, engineering, and biology, and study the effects of perturbations on these systems. The upshot is that even small perturbations can accumulate over time, giving rise to large effects, such as significant energy growth, and trajectories that wander far from their initial point. In particular, we will address conjectures proposed by Arnold (1964) and Chirikov (1979).
Location: Dinwiddie 108
Time: 3:30PM
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Thursday, February 19,
Colloquium
Title: TBA
Speaker: Michael Robinson - American University (Host: Rafal)
Abstract: TBA
Location: TBA
Time: 3:30
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Thursday, February 26,
Colloquium
Title: TBA
Speaker: Nancy Neudauer - Pacific University (Host: Mahir)
Abstract: TBA
Location: TBA
Time: 3:30
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Thursday, March 05,
Colloquium
Title: TBA
Speaker: Sergio R. López-Permouth - Ohio University (Host: Mahir)
Abstract: TBA
Location: TBA
Time: 3:30
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Thursday, March 12,
Colloquium
Title: TBA
Speaker: Bernhard Heim - Universitat Koln (Host: Olivia)
Abstract: TBA
Location: TBA
Time: 3:30
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Thursday, March 19,
Colloquium
Title: TBA
Speaker: Ivan Corwin - Columbia University (Host: Guido)
Abstract: TBA
Location: TBA
Time: 3:30
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Thursday, April 04,
Colloquium
Title: TBA
Speaker: Jayadev S. Athreya - University of Washington (Host: Kalina & Edna)
Abstract: TBA
Location: TBA
Time: 3:30
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Thursday, April 16,
Colloquium
Title: TBA
Speaker: Henry Adams - University of Florida (Host: Rafal)
Abstract: TBA
Location: TBA
Time: 3:30
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Thursday, April 23,
Colloquium
Title: TBA
Speaker: Nick Andersen - BYU (Host: Olivia)
Abstract: TBA
Location: TBA
Time: 3:30
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