Past Seminars

Spring 2021

Thursday, March 10, 2022, 1-2 pm

Zoom link:

Speaker: Prof. Johann Thiel (City Tech)

Title: Subgroups of SL_2(Z) characterized by certain continued fraction representations

Abstract: For positive integers u and v, let L_u = [1,0;u,1] and R_v = [1,v;0,1].  Let S_{u,v} be the monoid generated by L_u and R_v and G_{u,v} be the group generated by L_u and R_v.  The membership problem for S_{u,v} and G_{u,v} asks the following question: given a 2-by-2 matrix M = [a,b;c,d], is there a relatively straightforward method for determining if M is a member of S_{u,v} or G_{u,v}?  In the case where u=2 and v=2, Sanov was able to show that simply checking some divisibility conditions for a, b, c, and d is enough to make this determination.  In this talk, we will give an extension of a characterization of matrices in S_{k,k} and G_{k,k} when k >= 2 given by Esbelin and Gutan to S_{u,v} when u,v >= 2 and G_{u,v} when u,v >= 2 with uv != 4.  We will present a simple algorithmic way of determining the membership of M using a recursive function and the short continued fraction representation of b/d.


Fall 2021

Thursday, November 11, 2021, 1-2 pm

Zoom link:

Speaker: Prof. Hans Schoutens (City Tech)

Title: A pigeon wants to get in a hole…

Abstract: In MAT2540, our students learn about the Pigeonhole Principle (=more pigeons than holes means at least one of them has to share a hole); in MAT2580, our students study the Rank-nullity theorem, which implies that an injective linear self-map is also surjective, and conversely. Both principles have the same flavor and hold because we are in some finitary situation. Moving away from the finitary case, these principles normally fail. A famous example is Hotel Hilbert: on its website it lists that it is fully booked, but you can still order a room for the same day?!

I will give though some infinitary examples where the principle holds, perhaps only partially. Most of these cases either come from logic or can be proven using logic, as I will try to explain without using too much jargon: pigeons should be able to follow this talk 🙂


Spring 2021

Thursday, March 18, 2020, 1-2 PM

Speaker: Opening Gateways Team (City Tech)

Title: Teaching in the Times of COVID: Best Practices and Effective Assignments

Abstract: Join us as we share effective assignments and best practices developed for remote instruction. We’ll discuss the classroom experience and how they might be modified for use in the future.  If you have an assignment you might like to share, please have it handy! We look forward to a lively discussion and learning more about how your instruction has evolved.



Fall 2020

Thursday, October 22, 2020, 1-2 PM

Speaker: Prof. Lin Zhou (City Tech)

Title: Improving Efficacy of Online Teaching

Abstract: Online teaching has been adopted at City Tech since the outbreak of COVID19, and this remote mode is expected to be continued for at least another semester. Making teaching effective is therefore more challenging than ever. In this seminar, we will share experience of online teaching, including difficulties and possible solutions. Concerns arising from teacher-student interaction, class management, and effective assessment of students’ work will be discussed.



Spring 2020

Thursday, March 19, 2020, 1-2 PM in room N700 (cancelled due to COVID-19)

Speaker: Prof. Lin Zhou (City Tech)

Title: Improving Efficacy of Math Education in a High Tech Environment

Abstract: In this pedagogy seminar, we will share experience of using hardware and software resources that are available to us to improve math education at City Tech. Some concerns arising from mixing traditional teaching methods with technology, such as online homework system, monitors in the classroom, will also be discussed.


Fall 2019

Thursday, October 17, 2019, 1-2 PM in room N700

Speaker: Prof. Hans Schoutens (City Tech)

Title: Encoding graphs as fields

Abstract: In a recent paper, we described an effective/computable way of associating to a graph a unique field, so that from the latter, one can in turn retrieve the entire graph by solving a Diophantine problem. An earlier avatar of this problem (for cliques/complete graphs) used the Diophantine problem posed by Fermat’s Last Theorem. In this talk, I will explain how all of this works; without details, this can be done fairly elementary, so not much background will be required.


Spring 2019

Thursday, April 11, 2019, 1-2 PM in room N700

Speaker: Prof. Jonas Reitz (City Tech)

Title: Gödel’s Incompleteness: The most abused theorem in modern mathematics


“It is sometimes claimed to prove the existence of God or of free will, the necessary
incompleteness of the Bible or of the U.S. Constitution, or the impossibility
of genuine knowledge in mathematics—just to mention a few of the many alleged

– Panu Raatikainen, Notices of the AMS, March 2007

The goal of this talk is to give an overview of Gödel’s First
Incompleteness Theorem, exploring the precise formulation of this famous
result.  The talk will include an introduction to Mathematical Logic and
touch on some of the historical events in the field surrounding Gödel’s work.


Thursday, March 14, 2019, 1-2 PM in room N703

Speaker: Prof. Brad Isaacson (City Tech)

Title: Character sums and Bernoulli numbers

Abstract: We will examine a small collection of formulas expressing exponential sums or character sums by generalized Bernoulli numbers.  We often encounter such formulas when we compare the dimension formulas of modular forms in two different ways: by the Hirzebruch-Riemann-Roch theorem and the Selberg trace formula.  Often, the character sums or exponential sums appear in the first method and the generalized Bernoulli numbers appear in the second.  It is sometimes difficult to prove these relations in an elementary way, and in some cases, no elementary proof is known.  In this talk, we present some elementary methods to attack some of the easier problems.


Fall 2018

Thursday, October 11, 2018, 1-2 PM in room N700

Speaker: Prof. Nan Li (City Tech)

Title: Lipschitz-Volume rigidity

Abstract: We will begin with the following geometric questions.  1. Let A be a subset of metric space X with dim(X\A)<dim(X)-1. Is the metric completion of A always isometric to X? 2. Let X and Y be metric spaces and f:X->Y be a distance non-increasing and volume preserving onto map. Is f always an isometry?  The answers turn to be no for both questions in general. We will discuss the geometric conditions so that they can be true. As an application of these results, we get necessary conditions so that the gluing of convex spaces is still convex.


Spring 2018

Thursday, February 15, 2018, 1-2 PM, room N 720

Speaker: Prof Caner Koca (City Tech)

Title: Some Existence and Uniqueness Results for Solutions of Einstein’s Equations

Abstract: Riemannian Geometry is a popular branch of mathematics which is concerned with measuring quantities such as angles, lengths, areas, volumes, and above all, curvature of shapes, in all dimensions.

In the first part of the talk, I will give a picturesque survey of basic definitions and theorems in Riemannian Geometry; fundamental concepts such as Riemannian Metric, Gauss Curvature, Genus, Geodesics, Riemann Curvature Tensor, and Ricci Flow will be introduced with concrete examples. I will also describe Einstein’s Field Equations in General Relativity, which are a second order geometric PDE, whose Riemannian “no-boundary” solutions are of key interest in Sir Stephen Hawking’s quantum gravity program.

In the second part of the talk, I will present various existence and uniqueness results for Riemannian solutions of Einstein’s Field Equations which my collaborators and I proved in recent years.


Fall 2017

Thursday, October 16, 2017, 1-2 PM, Atrium Amphitheater AG 30

Speaker: Dava Sobel (Science Writer and author of “The Glass Universe”)

Title: The Glass Universe

Abstract: The Mathematics Colloquium will present a fascinating and engaging talk for students and faculty by distinguished science writer Dava Sobel. Her recently published best-selling book “The Glass Universe” tells the little-known story of Harvard’s female astronomers of the late 19th and 20th centuries and their national and international acclaim for their discoveries. The most famous among them—Williamina Fleming, Antonia Maury, Annie Jump Cannon, Henrietta Leavitt, and Cecilia Payne-Gaposchkin—are the heroines of this story. The work was not only performed by women, but also funded by female philanthropists.



Spring 2017

Thursday, May 11, 2017, 1-2 PM

Speaker: Prof. Frank Wattenberg (United States Military Academy West Point)

Title: Images, Mathematics, Imagination


Thursday, March 23, 2017, 1-2 PM

Speaker: Prof. Said Antonio Kas-Danouche Rojas (Universidad de Oriente, Venezuela)

Title: A mathematical model for a core-annular flow in pulmonary airways with an electrical field


Thursday, March 16, 2017, 1-2 PM

Speaker: Prof. Zaji Daugherty (City College, CUNY)

Title: Brauer algebras and their generalizations


Thursday, February 16, 2017, 1-2 PM

Speaker: Prof. Satanyand Singh (City Tech)

Title: Terms of lambda sequences over certain two element sets


Fall 2016

Thursday, November 10, 2016, 1-2 PM

Speaker: Prof. Kate Poirier (City Tech)

Title: Intersecting loops on surfaces and string topology


Thursday, October 20, 2016, 1-2 PM

Speaker: Prof. Mariya Bessonov (City Tech)

Title: Probabilistic models in population dynamics



Link to 2007-2013 Math Seminar Series:


Link to 2007-2012 Mathematics and Physics Colloquia: