Dedicated Teaching
8/30/23

Our faculty-student ratio is high compared to many universities. We teach students to develop skill-sets in computation, analysis, research, communication, practical problem solving, and mathematical modeling.

New: MS Program in Computational and Applied Mathematics
12/4/23
The demand for a professional labor force skilled in data analysis and statistical methods, alongside scientific computation and other applied mathematics techniques, and has grown tremendously over the last decade, and all indications are that such growth will further accelerate in the near future.
Algebra, Analysis, Calculus, Applied Mathematics, Geometry, Topology and more
4/26/22

Mathematics is a broad discipline with many diverse applications in physical sciences, life sciences, and engineering as well as social and managerial sciences. The Department of Mathematics provides a variety of concentrations leading to Baccalaureate, Masters, and PhD degrees.

Active Intellectual Life
4/26/22

The Department of Mathematics is proud of its excellent teaching and active research programs. Several of our faculty members are recipients of the SUNY Chancellor's Award for Excellence in Teaching. A strong tradition of mentorship attracts the most promising individuals and supports their development.

Faculty Research.
Faculty Research
4/25/22

Each year  about one-third of our faculty hold external research grants from agencies such as the U.S. Department of Defense, the National Security Agency, and the National Science Foundation. Faculty research enhances our intellectual and technological environment to support exceptionally creative science and education.

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Fall 2024 Events

Math Seminars

Join us for seminar and events:

Mon, Sep 16

Algebra Seminar
Anna Wysoczańska-Kula, Uniwersytet Wrocławski
Free resolution of universal unitary quantum groups
4:00PM, 250 Mathematics Building


Wed, Sep 18

Analysis Seminar
Wenbo Sun, Virginia Tech
Geometry Ramsey Conjecture over finite fields
4:00PM, 250 Math Building


Fri, Sep 20

Geometry and Topology Seminar
Matthew Stoffregen (Michigan State University)
TBA
4:00PM, 122 Mathematics Building


Mon, Sep 23

Algebra Seminar
Hecke algebras on homogeneous trees and relations with Hankel and Toeplitz matrices
Hecke algebras on homogeneous trees and relationswith Hankel and Toeplitz matrices Abstract : A homogeneous tree of degree \(q+1\) (a positive integer) is a connected graph, with no loops and with each vertex having exactly \(q+1\) neighbours. The distance \(d(x,y)\) between vertices \(x\) and \(y\) is the length of the uniquely defined geodesic connecting them.  In particular there are \((q+1)q^{n-1}\)vertices at distance \(n>0\) from a given one. In this talk we consider distance-dependent two-variable functions (kernels) \(f(x,y)\), defined on pairs of vertices. The Hecke algebra on homogeneous tree is a commutative algebra, spanned by particular kernels, defined on pairs of vertices \((x,y)\)and indexed by non-negative integers \(f_n(x,y)\). Each of these kernels depends on the distance between the vertices and vanishes if the distance is not equal to their index, otherwise it equals 1. We will show that the Hecke algebra is generated by \(f_1\), which satisfies quadratic (Hecke) equation. Our main interest is in showing that the Hecke algebra is MASA                      (i.e. Maximal Abelian SubAlgebra) in some bigger algebra. If \(q>1\) then a geometric trick of a Y-turn on the tree will do the job. If \(q=1\), which corresponds to the tree of integers, the      Y-turn is not possible, and we introduce some additional (Banach space)structure and show that the Hecke algebra is not MASA, but its commutant decomposes as a direct sum of Hankel and Toeplitz (double-infinite) matrices.
4:00PM, 250 Mathematics Building

Title: Hecke algebras on homogeneous trees and relationswith Hankel and Toeplitz matrices

 

Abstract : A homogeneous tree of degree \(q+1\) (a positive integer) is a connected graph, with no loops and with each vertex having exactly \(q+1\) neighbours. The distance \(d(x,y)\) between vertices \(x\) and \(y\) is the length of the uniquely defined geodesic connecting them.  In particular there are \((q+1)q^{n-1}\)vertices at distance \(n>0\) from a given one. In this talk we consider distance-dependent two-variable functions (kernels) \(f(x,y)\), defined on pairs of vertices.

 

The Hecke algebra on homogeneous tree is a commutative algebra, spanned by particular kernels, defined on pairs of vertices \((x,y)\)and indexed by non-negative integers \(f_n(x,y)\). Each of these kernels depends on the distance between the vertices and vanishes if the distance is not equal to their index, otherwise it equals 1. We will show that the Hecke algebra is generated by \(f_1\), which satisfies quadratic (Hecke) equation. Our main interest is in showing that the Hecke algebra is MASA                      (i.e. Maximal Abelian SubAlgebra) in some bigger algebra.

 

If \(q>1\) then a geometric trick of a Y-turn on the tree will do the job. If \(q=1\), which corresponds to the tree of integers, the      Y-turn is not possible, and we introduce some additional (Banach space)structure and show that the Hecke algebra is not MASA, but its commutant decomposes as a direct sum of Hankel and Toeplitz (double-infinite) matrices.


Wed, Sep 25

Analysis Seminar
Jakob Streipel, University of Maine
4:00PM, 250 Math Building


Fri, Sep 27

Applied Math Seminar
Mohammad-Ali Miri, Queens College CUNY
TBA.

3:00PM, Math 250


Wed, Oct 9

Analysis Seminar
Jingbo Xia, SUNY at Buffalo
The Helton-Howe trace formula for the Drury-Arveson space
4:00PM, 250 Math Building


Fri, Oct 18

Applied Math Seminar
Jia Zhao, Binghamton University
TBA.

3:00PM, Math 250


Wed, Oct 23

Analysis Seminar
Raphael Ponge, Sichuan University
4:00PM, 250 Math Building


Fri, Oct 25

Applied Math Seminar
Deniz Bilman, University of Cincinnati
TBA.

3:00PM, Math 250


Wed, Nov 13

Analysis Seminar
Joseph Leung, Rutgers University
4:00PM, 250 Math Building


Fri, Nov 22

Applied Math Seminar
Katerina Gkogkou, Tulane University
TBA.

3:00PM, Math 250


Related Calendars

Faculty Spotlight

  • Barbara Prinari, co-founder and deputy editor, Cambridge Journal of Nonlinear Waves
    9/9/24
    The UB Department of Mathematics is pleased to announce that Professor Barbara Prinari is co-founder and deputy editor of Cambridge Core's Journal of Nonlinear Waves. Prinari's research adds scope and depth to the journal's editorial board. Problems addressed by Prinari include the development of the Inverse Scattering Transform (IST) as a tool to solve the initial-value problem for scalar, vector and matrix continuous and discrete nonlinear Schrodinger (NLS) equations with both vanishing and nonvanishing boundary conditions at infinity; solitons and rogue wave solutions; vector soliton interactions, etc.  
  • Hanfeng Li named UB Distinguished Professor
    11/3/20
    Hanfeng Li has been named UB Distinguished Professor. His primary research interest is noncommutative geometry and dynamical systems, particularly connections between operator algebras and dynamical systems. A 2020 fellow of the American Mathematical Society (AMS), his recent work concentrates on actions of countable sofic groups and algebraic actions of general countable (amenable) groups. 
  • Badzioch wins SUNY Chancellor’s Award for Excellence in Teaching
    6/4/24
    Bernard Badzioch has won the 2024 SUNY Chancellor’s Award for Excellence in Teaching. Dr. Badzioch was recognized for consistently demonstrating superior teaching at the undergraduate and graduate level. As an innovative educator, students remark that Dr. Badzioch has the “rare skill, particularly amongst mathematicians,” to understand even their most incomprehensible questions and answer in a way that makes them feel good for having asked it. Read UBNow.
  • The power of stochastic differential equations
    5/8/24
    A new algorithm developed by Naoki Masuda, with co-athors Kazuyuki Aihara and Neil G. MacLaren, can identify the most predictive data points that a tipping point is near. Published in Nature Communications, this theoretical framework uses the power of stochastic differential equations to observe the fluctuation of data points, or nodes, and then determine which should be used to calculate an early warning signal. The algorithm is unique in that it fully incorporates network science into the process.
  • PNAS publishes collaborative research that sheds light on steep ocean wave dynamics
    11/3/20
    In a new collaborative study published in the Proceedings of the National Academy of Sciences (PNAS), a team of researchers from the University of Washington, SUNY at Buffalo and the University of New Mexico have unveiled the dominant mechanism behind wave-breaking of tall oceanic waves. The research team includes Prof. Bernard Deconinck (UW), Prof. Sergey Dyachenko (UB), Prof. Pavel Lushnikov (UNM) and Dr. Anastassiya Semenova (UW).
See all

YOUR MATH TUTOR IS HERE

UB MATH HELP CENTER

FREE AND OPEN TO STUDENTS 

Our students take advantage of free, in-person sessions  for math tutoring, advice, and resources to help them succeed in courses for MTH 121, 122, 131, 141, 142, 241, 306, 309, and more.  Learn more.

Our students

  • Destiny Diaz wins NSF Graduate Research Fellowship Award
    8/22/20
    The 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.
  • Linda Alegria, UB Math Graduate Student, wins Excellence in Teaching Award
    4/25/22
    The 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.
  • Yanyan Li presents research poster at SUNY conference and at UB's Celebration of Academic Excellence
    4/11/22
    Congratulations to UB Mathematics major Yanyan Li on being selected to present a research poster at two major events showcasing UB's undergraduate research excellence. Yanyan is studying gene co-expression networks under the guidance of her faculty mentor, Dr. Naoki Masuda. Specifically, she is deploying mathematical and computational methods for searching anomalous genes in networks of co-expression across different human organs, and how such genes may have evolutionary implications. Yanyan is one of the four awardees to present research at the SUNY 2022 Undergraduate Research Conference, held at Buffalo State College on April 23.  Yanyan will also present her work at UB's 18th Annual Celebration of Student Academic Excellence, on April 27, 2022. All are welcome to attend.
  • Yanyan Li presents research poster at SUNY conference and at UB's Celebration of Academic Excellence
    4/11/22
    Congratulations to UB Mathematics major Yanyan Li on being selected to present a research poster at two major events showcasing UB's undergraduate research excellence. Yanyan is studying gene co-expression networks under the guidance of her faculty mentor, Dr. Naoki Masuda. Specifically, she is deploying mathematical and computational methods for searching anomalous genes in networks of co-expression across different human organs, and how such genes may have evolutionary implications. Yanyan is one of the four awardees to present research at the SUNY 2022 Undergraduate Research Conference, held at Buffalo State College on April 23.  Yanyan will also present her work at UB's 18th Annual Celebration of Student Academic Excellence, on April 27, 2022. All are welcome to attend.
  • Miller and Scilla win the 2023 Montague Awards
    10/6/23
    The UB Department of Mathematics is pleased to announce that Alexandra Miller and Giacomo Scilla are the winners of the 2023 Harriet F. Montague Award. The award was established to commemorate the career of Dr. Montague, who was one of the early graduates the UB mathematics program, and who returned to chair the department for many years. The annual award is presented to one or more UB mathematics majors who have demonstrated intellectual and creative promise in mathematics. Of note, Giacomo Scilla is the recipient of the 2023 Summer Math Scholarship.
  • Giacomo Scilla wins the 2023 Summer Math Scholarship
    3/16/23
    The UB Department of Mathematics is pleased to announce that Giacomo Scilla is the recipient of the 2023 Summer Math Scholarship. Together with faculty mentor Dr. Gino Biondini, Scilla formulated an undergraduate research project aimed at understanding the classification of two-dimensional wave patterns governed by the solutions of the Kadomtsev-Petviashvili equation, with the ultimate goal of deriving efficient methods to generate large ensembles of such solutions.
See all

Mon, Sep 16

Algebra Seminar
Anna Wysoczańska-Kula, Uniwersytet Wrocławski
Free resolution of universal unitary quantum groups
4:00PM, 250 Mathematics Building


Wed, Sep 18

Analysis Seminar
Wenbo Sun, Virginia Tech
Geometry Ramsey Conjecture over finite fields
4:00PM, 250 Math Building


Fri, Sep 20

Geometry and Topology Seminar
Matthew Stoffregen (Michigan State University)
TBA
4:00PM, 122 Mathematics Building


Mon, Sep 23

Algebra Seminar
Hecke algebras on homogeneous trees and relations with Hankel and Toeplitz matrices
Hecke algebras on homogeneous trees and relationswith Hankel and Toeplitz matrices Abstract : A homogeneous tree of degree \(q+1\) (a positive integer) is a connected graph, with no loops and with each vertex having exactly \(q+1\) neighbours. The distance \(d(x,y)\) between vertices \(x\) and \(y\) is the length of the uniquely defined geodesic connecting them.  In particular there are \((q+1)q^{n-1}\)vertices at distance \(n>0\) from a given one. In this talk we consider distance-dependent two-variable functions (kernels) \(f(x,y)\), defined on pairs of vertices. The Hecke algebra on homogeneous tree is a commutative algebra, spanned by particular kernels, defined on pairs of vertices \((x,y)\)and indexed by non-negative integers \(f_n(x,y)\). Each of these kernels depends on the distance between the vertices and vanishes if the distance is not equal to their index, otherwise it equals 1. We will show that the Hecke algebra is generated by \(f_1\), which satisfies quadratic (Hecke) equation. Our main interest is in showing that the Hecke algebra is MASA                      (i.e. Maximal Abelian SubAlgebra) in some bigger algebra. If \(q>1\) then a geometric trick of a Y-turn on the tree will do the job. If \(q=1\), which corresponds to the tree of integers, the      Y-turn is not possible, and we introduce some additional (Banach space)structure and show that the Hecke algebra is not MASA, but its commutant decomposes as a direct sum of Hankel and Toeplitz (double-infinite) matrices.
4:00PM, 250 Mathematics Building

Title: Hecke algebras on homogeneous trees and relationswith Hankel and Toeplitz matrices

 

Abstract : A homogeneous tree of degree \(q+1\) (a positive integer) is a connected graph, with no loops and with each vertex having exactly \(q+1\) neighbours. The distance \(d(x,y)\) between vertices \(x\) and \(y\) is the length of the uniquely defined geodesic connecting them.  In particular there are \((q+1)q^{n-1}\)vertices at distance \(n>0\) from a given one. In this talk we consider distance-dependent two-variable functions (kernels) \(f(x,y)\), defined on pairs of vertices.

 

The Hecke algebra on homogeneous tree is a commutative algebra, spanned by particular kernels, defined on pairs of vertices \((x,y)\)and indexed by non-negative integers \(f_n(x,y)\). Each of these kernels depends on the distance between the vertices and vanishes if the distance is not equal to their index, otherwise it equals 1. We will show that the Hecke algebra is generated by \(f_1\), which satisfies quadratic (Hecke) equation. Our main interest is in showing that the Hecke algebra is MASA                      (i.e. Maximal Abelian SubAlgebra) in some bigger algebra.

 

If \(q>1\) then a geometric trick of a Y-turn on the tree will do the job. If \(q=1\), which corresponds to the tree of integers, the      Y-turn is not possible, and we introduce some additional (Banach space)structure and show that the Hecke algebra is not MASA, but its commutant decomposes as a direct sum of Hankel and Toeplitz (double-infinite) matrices.


Wed, Sep 25

Analysis Seminar
Jakob Streipel, University of Maine
4:00PM, 250 Math Building


Fri, Sep 27

Applied Math Seminar
Mohammad-Ali Miri, Queens College CUNY
TBA.

3:00PM, Math 250


Wed, Oct 9

Analysis Seminar
Jingbo Xia, SUNY at Buffalo
The Helton-Howe trace formula for the Drury-Arveson space
4:00PM, 250 Math Building


Fri, Oct 18

Applied Math Seminar
Jia Zhao, Binghamton University
TBA.

3:00PM, Math 250


Wed, Oct 23

Analysis Seminar
Raphael Ponge, Sichuan University
4:00PM, 250 Math Building


Fri, Oct 25

Applied Math Seminar
Deniz Bilman, University of Cincinnati
TBA.

3:00PM, Math 250


Wed, Nov 13

Analysis Seminar
Joseph Leung, Rutgers University
4:00PM, 250 Math Building


Fri, Nov 22

Applied Math Seminar
Katerina Gkogkou, Tulane University
TBA.

3:00PM, Math 250


Our Alumni

Learn more

UB Office of Equity, Diversity, and Inclusive Excellence

Realizing full potential

UB is committed to achieving inclusive excellence in a deliberate, intentional and coordinated fashion, embedding it in every aspect of our operations. We aspire to foster a healthy, productive, ethical, fair, and affirming campus community to allow all students, faculty and staff to thrive and realize their full potential. 

UB Math Spotlight

  • Barbara Prinari, co-founder and deputy editor, Cambridge Journal of Nonlinear Waves
    9/9/24
    The UB Department of Mathematics is pleased to announce that Professor Barbara Prinari is co-founder and deputy editor of Cambridge Core's Journal of Nonlinear Waves. Prinari's research adds scope and depth to the journal's editorial board. Problems addressed by Prinari include the development of the Inverse Scattering Transform (IST) as a tool to solve the initial-value problem for scalar, vector and matrix continuous and discrete nonlinear Schrodinger (NLS) equations with both vanishing and nonvanishing boundary conditions at infinity; solitons and rogue wave solutions; vector soliton interactions, etc.  
  • Hanfeng Li named UB Distinguished Professor
    11/3/20
    Hanfeng Li has been named UB Distinguished Professor. His primary research interest is noncommutative geometry and dynamical systems, particularly connections between operator algebras and dynamical systems. A 2020 fellow of the American Mathematical Society (AMS), his recent work concentrates on actions of countable sofic groups and algebraic actions of general countable (amenable) groups. 
  • Badzioch wins SUNY Chancellor’s Award for Excellence in Teaching
    6/4/24
    Bernard Badzioch has won the 2024 SUNY Chancellor’s Award for Excellence in Teaching. Dr. Badzioch was recognized for consistently demonstrating superior teaching at the undergraduate and graduate level. As an innovative educator, students remark that Dr. Badzioch has the “rare skill, particularly amongst mathematicians,” to understand even their most incomprehensible questions and answer in a way that makes them feel good for having asked it. Read UBNow.
  • The power of stochastic differential equations
    5/8/24
    A new algorithm developed by Naoki Masuda, with co-athors Kazuyuki Aihara and Neil G. MacLaren, can identify the most predictive data points that a tipping point is near. Published in Nature Communications, this theoretical framework uses the power of stochastic differential equations to observe the fluctuation of data points, or nodes, and then determine which should be used to calculate an early warning signal. The algorithm is unique in that it fully incorporates network science into the process.
  • PNAS publishes collaborative research that sheds light on steep ocean wave dynamics
    11/3/20
    In a new collaborative study published in the Proceedings of the National Academy of Sciences (PNAS), a team of researchers from the University of Washington, SUNY at Buffalo and the University of New Mexico have unveiled the dominant mechanism behind wave-breaking of tall oceanic waves. The research team includes Prof. Bernard Deconinck (UW), Prof. Sergey Dyachenko (UB), Prof. Pavel Lushnikov (UNM) and Dr. Anastassiya Semenova (UW).
  • Giacomo Scilla wins the 2023 Summer Math Scholarship
    3/16/23
    The UB Department of Mathematics is pleased to announce that Giacomo Scilla is the recipient of the 2023 Summer Math Scholarship. Together with faculty mentor Dr. Gino Biondini, Scilla formulated an undergraduate research project aimed at understanding the classification of two-dimensional wave patterns governed by the solutions of the Kadomtsev-Petviashvili equation, with the ultimate goal of deriving efficient methods to generate large ensembles of such solutions.
  • Robert Busch wins Milton Plesur Excellence in Teaching Award
    5/24/22
    The 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.”
  • Professor Naoki Masuda wins JSPS Prize
    2/26/20
    The 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.
  • Destiny Diaz wins NSF Graduate Research Fellowship Award
    8/22/20
    The 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.
  • UB Math Grads win NSF Graduate Research Fellowships
    6/4/16
    The 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.