Geometry and Topology Seminar**Yuan Yao (UC Berkeley)**

TBA

4:00PM, 122 Mathematics Building

Algebra Seminar**Mariusz Tobolski, University of Wroclaw**

Cohomology of free unitary quantum groups

4:00PM, Mathematics Building room 250

In this talk, I will present the Hochschild and bialgebra cohomology with 1-dimensional coefficients of the \(*\)-algebras associated with free universal unitary quantum groups. The result is based on the free resolution of the counit of the free orthogonal quantum groups found by Collins, Härtel, and Thom which was then generalized by Bichon to the case of quantum groups associated with a nondegenerate bilinear form. In fact, we compute cohomology groups of the universal cosovereign Hopf algebras, which generalize free unitary quantum groups and are connected to quantum groups of non-degenerate bilinear forms. This is a joint work with U. Franz, M. Gerhold,A. Wysocza\'nska-Kula, and I. Baraquin.

Algebra Seminar**Robert Corless, Western University**

Bohemian Matrix Geometry

4:00PM, Mathematics Building room 250

A Bohemian matrix family is a set of matrices all of whose entries are drawn from a fixed, usually discrete and hence bounded, subset of a field of characteristic zero. Originally these were integers---hence the name, from the acronym BOunded HEight Matrix of Integers(BOHEMI)---but other kinds of entries are also interesting. Some kinds of questions about Bohemian matrices can be answered by numerical computation, but sometimes exact computation is better. In this paper we explore some Bohemianfamilies (symmetric, upper Hessenberg, or Toeplitz) computationally, and answer some (formerly) open questions posed about the distributions of eigenvalue densities.

This work connects with several disparate areas of mathematics, including dynamical systems, combinatorics, probability and statistics, and number theory. Because the thinking about the topic is so recent, most of the material is still quite exploratory, and this talk will be accessible to students as well as to faculty. Several open problems remain open, and I would welcome your thoughts on them.

This is joint work with several people, including EuniceY.S. Chan, Leili Rafiee Sevyeri, Neil J. Calkin, Piers W. Lawrence, Laureano Gonzalez-Vega, Dan Piponi, Juana Sendra, and Rafael Sendra.

Geometry and Topology Seminar**Nima Hoda (Cornell University)**

TBA

4:00PM, 122 Mathematics Building

Algebra Seminar**Ana Agore, Max Planck Institut and Simion Stoilow Institute of Mathematics**

Universal constructions for Poisson algebras. Applications.

9:00AM, Zoom (please email achirvas@buffalo.edu)

We introduce the universal algebra of two Poisson algebras \(P\) and \(Q\) as a commutative algebra \(A := \mathcal{P}(P, Q)\) satisfying a certain universal property. The universal algebra is shown to exist for any finite-dimensional Poisson algebra \(P\) and several of its applications are highlighted. For any Poisson \(P\)-module \(U\), we construct a functor \(U\otimes-: {}_A\mathcal{M} \to {}_Q\mathcal{PM}\) from the category of \(A\)-modules to the category of Poisson \(Q\)-modules which has a left adjoint whenever \(U\) is finite-dimensional. Similarly, if \(V\) is an \(A\)-module, then there exists another functor \(-\otimes V:{}_P\mathcal{PM}\to {}_Q\mathcal{QM}\) connecting the categories of Poisson representations of \(P\) and \(Q\) and the latter functor also admits a left adjoint if \(V\) is finite-dimensional. If \(P\) is\(n\)-dimensional, then \(\mathcal{P}(P) := \mathcal{P}(P, P)\) is the initial object in the category of all commutative bialgebras coacting on \(P\). As an algebra,\(\mathcal{P}(P)\) can be described as the quotient of the polynomial algebra\(k[X_{ij} | i, j = 1, · · · , n]\) through an ideal generated by \(2n^3\)non-homogeneous polynomials of degree \(\le 2\). Two applications are provided. The first one describes the automorphisms group\(\mathrm{Aut}_{\mathrm{Poiss}}(P)\) as the group of all invertible group-like elements of the finite dual \(\mathcal{P}(P)^{\circ}\). Secondly, we show that for an abelian group\(G\), all \(G\)-gradings on \(P\) can be explicitly described and classified in terms of the universal coacting bialgebra \(\mathcal{P}(P)\). Joint work with G.Militaru.

Applied Math Seminar**Boaz Ilan, UC Merced**

TBA

2:00PM, Zoom - contact mbichuch@buffalo.edu for link

Colloquium**Bena Tshishiku (Brown University)**

4:00PM, 250 Mathematics Building

Geometry and Topology Seminar**Bena Tshishiku (Brown University)**

4:00PM, 122 Mathematics Building

Geometry and Topology Seminar**Reserved**

4:00PM, 122 Mathematics Building

**FREE AND OPEN TO STUDENTS **

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- 11/3/20
**Mapping neuron-to-neuron communication:**Dane Taylor, PhD, assistant professor of mathematics, and UB PhD candidate Bengier Ulgen Kilic conduct research to better understand the biological and mathematical mechanisms that allow brains to manifest memories as neuron activity patterns that can be stored and reliably called upon later for cognitive processing.**"Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes"**is the resulting paper published by*Nature, Communications Physics*. The international journal is called "the finest peer-reviewed research in all fields of science and technology on the basis of its originality, importance, interdisciplinary interest, timeliness, accessibility, elegance and surprising conclusions." Read research news by Barbara Branning. - 4/25/22The Department of Mathematics is pleased to announce that Linda Alegria has been awarded the University at Buffalo's 2022 Excellence in Teaching Award for Graduate Student Teaching Assistants. The award was presented at a luncheon in April, with Satish Tripathi, UB President, and Robin Schulze, CAS Dean, in attendance.
- 3/31/22The University at Buffalo Department of Mathematics is pleased to announce that Julia Shapiro, winner of the 2022 SUNY Chancellor's Award for Student Excellence. Shapiro will graduate with a bachelor of science in mathematics, and her accomplishments as an undergraduate student include: University Honors College Scholar, winner of the 2021 Harriet F. Montague Award, and President of the UB Undergraduate Math Club. Shapiro has completed research on Markov Chains through a nationally recognized program at the University of Connecticut, has been a Peer Mentor in the Honors College, has served as an Ambassador of both the Honors College and the College of Arts and Sciences, and has served as an Undergraduate Teaching Assistant in three separate departments — Mathematics, Biostatistics, and Computer Science.
- 11/3/20Statisticians from across upstate New York will descend on UB May 2-4 for UP-STAT 2022, the 10th joint conference of the Upstate Chapters of the American Statistical Association. Sarah Muldoon, associate professor in the Department of Mathematics, UB College of Arts and Sciences, will deliver a special invited session on modeling and analyzing neuroimaging data across scales. Visit the conference website. Read the story by David J. Hill.
- 11/3/20CNN Health—We really did buy more alcohol during the early pandemic, study finds: As many U.S. states implemented stay-at-home orders beginning in March 2020, anecdotes reported a surge in alcohol sales, raising concerns about increased alcohol use and associated ills. The surveillance report from the National Institute on Alcohol Abuse and Alcoholism provides monthly U.S. alcohol sales data from a subset of states, allowing an investigation of this potential increase in alcohol use. Meanwhile, anonymized human mobility data released by companies such as SafeGraph enables an examination of the visiting behavior of people to various alcohol outlets such as bars and liquor stores. The study's coauthors are: Yingjie Hu, assistant professor in the department of geography; Brian Quigley, a research assistant professor of medicine in the Jacobs School of Medicine and Biomedical Sciences; and, Dane Taylor, assistant professor in the department of mathematics. Their study examines changes to alcohol sales and alcohol outlet visits during COVID-19 and their geographic differences across states. See research news by Charlotte Hsu.

- 1/11/22The UB Department of Mathematics is pleased to announce that Tyler Glover, a junior majoring in Mathematics, is the recipient of the 2021 Math Summer Scholarship. Under the guidance faculty mentor, Dr. Joseph Hundley, Tyler designed a special Undergraduate Research project that involved studying methods of geometric construction beyond the standard straight edge and compass, as well as their limitations and the number systems associated with them. For example, a classic result of abstract algebra states that if a segment of length x can be constructed, given a straight edge, a compass, and a segment of length 1, then x must be a root of an irreducible polynomial with integer coefficients and degree equal to a power of two.
- 5/24/22The Department of Mathematics is pleased to announce that Robert Busch, clinical assistant professor, is the winner of the coveted Milton Plesur Excellence in Teaching Award, 2019-2020. Busch was recognized by the undergraduate Student Association for his commitment and dedication to students. He was nominated for the award by his students. Upon news of the award, Busch's first thought was to acknowledge his students: “To all my students, over all the years, and in all the classes…for giving me the privilege of being your instructor, for making me into a better teacher, communicator, and human being, for the pleasure of watching you learn and succeed, and for the thrill of seeing you graduate and step into your dreams…from the bottom of my heart…THANK YOU.”
- 8/22/20The University at Buffalo Department of Mathematics is pleased to announce that Destiny Diaz has won the National Science Foundation’s Graduate Research Fellowship Award. The prestigious award is one of the most competitive and respected scientific fellowships in the U.S. Diaz is completing a BS in mathematics with a minor in Spanish. Recently, Diaz received 2019 SUNY Chancellor’s Award for Student Excellence. A Buffalo native, she is a member of the University Honors College and a Prosperity Fellow. In Fall 2019, the NSF Graduate Research Fellowship will support her pursuit of graduate study in biostatistics at UB. The award provides three years of financial support within a five-year fellowship period, which amounts to a $34,000 annual stipend and $12,000 cost-of-education allowance to the graduate institution.
- 1/11/22Congratulations to UB Mathematics major Mengyuan (Jason) Sun on being selected to present a research poster in the 2021 Celebration of Student Academic Excellence Poster Presentations". His work is titled "Synthesis of Doped 2d Transition Metal Chalcogenide". Sun will deliver an 8-minute oral presentation via Zoom, Wednesday, April 21. Everyone is welcome to attend the virtual event. UB Mathematics students who may be interested in doing their own research project or presentation in the future are particularly encouraged to attend. Learn more about the Celebration of Student Academic Excellence, and see messages from President Tripathi and Provost Weber, here. See the full schedule of the poster sessions, here.
- 6/4/16The National Science Foundation Graduate Research Fellowship Program (GRFP) named a record number of winners from UB this year, one more than all the awards given to students in the rest of the SUNY system. For the 2016 competition, NSF received close to 17,000 applications, and made 2,000 award offers.
- 2/26/20The University at Buffalo Department of Mathematics is pleased to announce that Dr. Naoki Masuda, Associate Professor, is the winner of the JSPS (Japan Society for Promotion of Science) Prize 2020. The national award recognizes his work, “Pioneering Research on Theory and Data-Analysis Methods for Temporal Networks”. Dr. Masuda attended the JSPS Awards Ceremony in February, 2020, accompanied by his daughter, Ami Masuda. The JSPS 2020 Award included full funding of their travel to Japan. While there, Dr. Masuda and Ami participated in an exclusive audience with the Japanese Royal Family.