Fri, Mar 29
Geometry and Topology Seminar
Carolyn Abbott (Brandeis University)
Morse boundaries of CAT(0) cubical groups
4:00PM, 122 Mathematics Building
The visual boundary of a hyperbolic space is a quasi-isometry invariant that has proven to be a very useful tool in geometric group theory. When one considers CAT(0) spaces, however, the situation is more complicated, because the visual boundary is not a quasi-isometry invariant. Instead, one can consider a natural subspace of the visual boundary, called the (sublinearly) Morse boundary. In this talk, I will describe a new topology on this boundary and use it to show that the Morse boundary with the restriction of the visual topology is a quasi-isometry invariant in the case of (nice) CAT(0) cube complexes. This result is in contrast to Cashen’s result that the Morse boundary with the visual topology is not a quasi-isometry invariant of CAT(0) spaces in general. This is joint work with Merlin Incerti-Medici.
Wed, Apr 3
Analysis Seminar
Liang Guo, East China Normal University
Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture
4:00PM, 250 Math Building
The equivariant coarse Novikov conjecture synthesizes all the Novikov-type conjectures, including the strong Novikov conjecture for groups and the coarse Novikov conjecture for metric spaces. It has fruitful applications in topology and geometry. In a recent work of Sherry Gong, Jianchao Wu, and Guoliang Yu, a notion of Hilbert-Hadamard space is introduced to study the Novikov conjecture for specific groups, which can be seen as an infinite-dimensional Hadamard manifold. To generalize their idea to the equivariant coarse Novikov conjecture, in this talk, we study a dynamic system that admits an equivariant coarse embedding into an admissible Hilbert-Hadamard space. I will start with several applications of the equivariant Novikov conjecture and show that the equivariant coarse Novikov conjecture holds for such a dynamic system. This is based on a joint work with Qin Wang, Jianchao Wu, and Guoliang Yu.
Wed, Apr 10
Algebra Seminar
Joe Kramer-Miller, Lehigh University
Transcendental properties of the Artin-Hasseexponential modulo p Abstract : The Artin-Hasse exponential is a p-adic analogue to the classical exponential function. It is ubiquitous in p-adic analysis, where it plays a pivotal role in the construction of Witt vectors and in Dwork theory. The miracle of the Artin-Hasse exponential is that its Taylor expansion has p-integral coefficients, and thus may be reduced modulo p. In this talk I will discuss recent work on the transcendental properties of the Artin-Hasse exponential mod p. We give two proofs that the Artin-Hasse exponential mod p is transcendental, answering a long-outstanding question posed by Thakur. We also explain several algebraic independence results for the Artin-Hasse exponential evaluated at different polynomials.
3:00PM, Mathematics Building, Buffalo
Title: Transcendental properties of the Artin-Hasseexponential modulo p
Abstract : The Artin-Hasse exponential is a p-adic analogue to the classical exponential function. It is ubiquitous in p-adic analysis, where it plays a pivotal role in the construction of Witt vectors and in Dwork theory. The miracle of the Artin-Hasse exponential is that its Taylor expansion has p-integral coefficients, and thus may be reduced modulo p. In this talk I will discuss recent work on the transcendental properties of the Artin-Hasse exponential mod p. We give two proofs that the Artin-Hasse exponential mod p is transcendental, answering a long-outstanding question posed by Thakur. We also explain several algebraic independence results for the Artin-Hasse exponential evaluated at different polynomials.
Wed, Apr 10
Analysis Seminar
Wencai Liu, Texas A&M University
Algebraic geometry, complex analysis and combinatorics in spectral theory of periodic graph operators
4:00PM, 250 Math Building
In this talk, we will discuss the significant role that the algebraic and analytic properties of complex Bloch and Fermi varieties play in the study of periodic operators. I will begin by highlighting recent discoveries about these properties, especially their irreducibility. Then, I will show how we can use these findings, together with techniques from complex analysis and combinatorics, to study spectral and inverse spectral problems arising from periodic operators.
Fri, Apr 12
Applied Math Seminar
Alexandr Chernyavskiy, UB
Dark-bright soliton perturbation theory for the Manakov system.
3:00PM, Math 122
A direct perturbation method for studying dynamics of
dark-bright solitons of the Manakov system in the presence of
perturbations is presented. We combine multiscale expansion method,
perturbed conservation laws, and a boundary layer approach, which breaks
the problem into an inner region, where the bulk of the soliton resides,
and an outer region, which evolves independently of the soliton. We show
that a shelf develops around the dark soliton component, with speed of the
shelf proportional to the background intensity. Conservation laws of
the Manakov system are used to determine the properties of the shelf and
perturbed solutions. Our analytical predictions are corroborated by
numerical simulations..
Fri, Apr 12
Geometry and Topology Seminar
Indira Chatterji (University of Côte d'Azur / Fields Institute)
TBA
4:00PM, 122 Mathematics Building
TBA
Fri, Apr 19
Applied Math Seminar
Anna Vainchtein, University of Pittsburgh
TBA.
3:00PM, Math 122 and on Zoom - contact mbichuch@buffalo.edu for link
TBA.
Wed, Apr 24
Colloquium
Tomasz Mrowka, MIT
2023-24 Myhill Lecture #1
4:00PM
Title: 2023-24 Myhill Lecture #1
Thu, Apr 25
Colloquium
Tomasz Mrowka, MIT
2023-24 Myhill Lecture #2
4:00PM
Title: 2023-24 Myhill Lecture #2
Fri, Apr 26
Colloquium
Tomasz Mrowka, MIT
2023-24 Myhill Lecture #3
4:00PM
Title: 2023-24 Myhill Lecture #3
Fri, May 3
Applied Math Seminar
Willy Hereman, Colorado School of Mines
TBA.
3:00PM, Math 122 and on Zoom - contact mbichuch@buffalo.edu for link
TBA.