Schedule (ET):

10:00 am Welcome (4th Floor Science Center)

10:10 am - 11:00 am: Keynote Speaker: Alena Erchenko (Dartmouth College) 
(4th Floor Science Center)

Zoom plenary 1

11:15 - 12:45: Contributed Talks (Parallel Sessions in Rooms 9206 and 9207)
Each talk is 20 - 23 minutes maximum with a few minutes for questions and a few minutes break.  Please prepare your talk for a general audience of mathematicians.

Morning Session I  (Room 9206) 
11: 15: Winnie Zhou (Wellesley College)
11:45: Raeann Kyriakou (St. Francis College)  
12:15: D. Tony Sün (Yeshiva University)
12:45:  Rohit Parikh (CUNY Graduate Center and Brooklyn College)

Morning Session II (Room 9207)

11: 15: Susan Rutter (CUNY Graduate Center)  
11:45: Jasmine Tom (Graduate Center)   
12:15: Megha Bhat (CUNY Graduate Center)  
12:45:  Siobhan O’Connor (Graduate Center) 

1:15 - 2:00 Lunch (4th Floor Math Lounge)

2:00 - 2:50: Keynote Speaker: Olympia Hadjiliadis (CUNY Graduate Center and Hunter College)
(4th Floor Science Center)

Zoom plenary 2

3:00 - 5:30: Contributed Talks (Parallel Sessions in Rooms 9206 and 9207)
Each talk is 20 - 23 minutes maximum with a few minutes for questions and a few minutes break.  Please prepare your talk for a general audience of mathematicians.

Afternoon Session I (Room 9206)

3:00: Sanjana Paul (Smith College)
3:30: John T. Saccoman (Seton Hall University)
4:00: Abigail Raz (Cooper Union)
4:30: Nadia Benakli (New York City College of Technology, CUNY)
5:00: Nhat-Dinh Nguyen (City College of New York, CUNY)

Afternoon Session II (Room 9207)

3:00: Torhira Oshoriameh Aminu (Bowie State University)  
3:30: Lubna Kadhim (Morgan State University)  
4:00: Nilava Metya (Rutgers University)  
4:30: Sayantika Mondal (CUNY Graduate Center)
5:00: Emma Dinowitz (CUNY Graduate Center)

5:30 pm - 6:00 pm: Wine and Cheese Social (4th Floor Math Lounge)

Titles and Abstracts:

Keynote Speaker: Alena Erchenko (Dartmouth College) 

Title: Geometric flexibility and rigidity of Anosov manifolds

Abstract: An Anosov manifold with boundary is a compact smooth Riemannian manifold M with strictly convex boundary, hyperbolic trapped set (possibly empty), and no conjugate points. We will discuss the marked boundary distance rigidity conjecture for Anosov manifolds with boundary and how to prove new cases using isometric extensions to closed Riemannian manifolds. This talk is based on joint work with Thibault Lefeuvre as well as joint work with Dong Chen and Andrey Gogolev.

Keynote Speaker: Olympia Hadjiliadis (CUNY Graduate Center and Hunter College)
Title: A Speed-based Estimator of Signal-to-Noise Ratios
Abstract: We present an innovative estimator of the signal-to-noise ratio (SNR) in a Brownian motion model. That is, the ratio of the mean to the standard deviation of the Brownian motion. Our method is based on the method of moments estimation of the drawdown and drawup speeds in a Brownian motion model, where the drawdown process is defined as the current drop of the process from its running maximum and the drawup process is the current rise of the process above its running minimum. The speed of a drawdown of K units (or a drawup of K units) is then the time between the last maximum (or minimum) of the process and the time the drawdown (or drawup) process hits the threshold K. We compare our estimator to traditional ones. Numerical results show that our estimator consistently outperforms some traditional estimators but not the uniformly minimum-variance unbiased estimator. However, we discuss cases in which the statistic related to our estimator can be useful. This is when the SNR changes in a real-time observation stream and the problem is jointly detecting and estimating the pre-and-post SNR’s. We finally present the asymptotic distribution of our estimator. This is joint work with Yuang Song.

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Morning Session I

1) Winnie Zhou (Wellesley College) canceled unfortunately
Title: Mathematics and Democracy: Simple and Weighted Voting from Topological and Category-Theoretic Perspectives
Abstract: In this research, conducted as part of the Mathematics and Democracy Institute fellowship program, we explore voting games through the lenses of topology and category theory. Building upon Hans Keiding's work on constructing voting games using category theory, we analyze the simplicial complex of losing coalitions to understand how a game's self-duality corresponds to the Alexander dual of the simplicial complex. We begin by examining the simplicial complex structures of games involving special voter roles—such as vetoers, passers, dummies, and dictators. We then investigate the properties of strongness and properness that constitute a game's self-duality and their correspondence to the structure of the simplicial complex. Currently, we are analyzing how the number-theoretic aspects of weights in weighted voting games relate to the game's duality. This is joint work with Arial and Professor Ismar Volic. 

2) Raeann Kyriakou (St. Francis College)
Title: Exploring the beauty of mathematics through games
Abstract:

3) D. Tony Sün (Yeshiva University)
Title: A Follow-Up Reflective Argument on Collegiate Mathematics Literacy in the Jewish Education Context: One Year After the Assisted Linear Algebra Classroom
Abstract:  Classrooms that are both modern and urban in math courses, especially beyond the freshman collegiate level, are seemingly expected more as a role of preparatory training for "literacy skills" such as quantitative writing, applying the real-world problems, and interpersonal scientific communication in forms of group projects and presentations. This is nonetheless a pedagogical, if not singular nor pragmatic, view that is wishful but in fact important as a reiteration in today's climate of collegiate education. Young women students of science and mathematics normally have a longer patience and attention span and a baseline reputation of completing the curriculum well and keeping good learning habits, however how to (re)examine the role(s) of university math courses in students' collegiate curricula remains yet a neccessity, in terms of both sustaining motivation and solidifying the quality of the curriculum itself. With a Jewish education as environment regarding the bachelor's degree programs relevant to math and computing, this reflection and argument attempts to provide what the author observes in the past two to three semesters as course assistant and occasional peer classmate to students in more than three recent courses, following his presentation here last year, about the same features and observations based on his somehow minute lens. Based on the individual student's academic and economic expectations, it is argued that an iterative refinement paradigm to course- and notes-taking is exclusively beneficial to the parallelism between a religious tradition and contemporary pursuits.

4)  Rohit Parikh (CUNY Graduate Center and Brooklyn College)

Title: The Logic of Social Choice

Abstract: Democracies want the government to be decided by the will of the people. But how is this "will of the people" to be defined?  Some problems were discovered by Marquis de Condorcet in France in the 18th century.  These problems received a mathematical form in Kenneth Arrow's famous theorem.  (Arrow was a CCNY graduate) But there are other issues with the American system. If Ralph Nader had not entered the race in 2000, Al Gore, the popular favorite would have been elected. In 2008, John McCain received several million individual votes in California but not a single electoral vote from California. Moreover, when we voters enter the voting booth, much of the action has already taken place. There are two leading candidates nominated by the parties. If we are not happy with that choice, tough luck. We make some suggestions for a reform of electoral systems.
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Morning Session II

5)  Susan Rutter (CUNY Graduate Center)
Title: Intro to Khovanov Homology
Abstract: Are you a student considering learning about Khovanov homology? Come to this talk for a short introduction to the field. We will mostly cover the definitions and key theorems that make it a useful theory, but will touch on current research and directions, including the questions I am thinking about.

6) Jasmine Tom (Graduate Center)
Title: An Introduction to Mapping Class Groups
Abstract: In Abstract Algebra, we study the group of symmetries of finite sets via the symmetric group Sn. In this talk, we provide an introduction to the mapping class group, which is the group of the symmetries of a surface. Firstly, we consider a special example of a homeomorphism between surfaces, that is, a Dehn twist. We define a Dehn twist on an annulus and then extend the notion to a Dehn twist about a simple closed curve on a surface. Next, we give examples of trivial mapping class groups and explore a mapping class group of infinite order, namely that of an annulus. Lastly, we conclude that Dehn twists are important elements of the mapping class group. In fact, they generate the mapping class group of a compact orientable surface.

7)  Megha Bhat (CUNY Graduate Center)
Title: Homeomorphisms and infinities
Abstract: The maximal normal subgroup of N is known to be the subgroup of all finite permutations, as shown in a classical result of Schreier and Ulam.  Further, Bergman showed that N is strongly bounded, that is, any left-invariant metric has bounded diameter.  Notably, N is isomorphic to the homeomorphism group of the first infinite successor ordinal \omega+1, equipped with the order topology.  We investigate whether these properties extend to groups of homeomorphisms of larger ordinals.  Restricting to a class of successor ordinals, we classify the ordinals for which these properties have natural generalizations.  Consequently, we recover the results regarding N using techniques from the study of homeomorphism groups of manifolds.   

8)  Siobhan O’Connor (Graduate Center)
Title: Orbit Blocking Words in Free Groups
Abstract: Given a word u in a free group does there always exist a word v that doesn’t appear as a subword of phi(u) for any automorphism phi? We show that the answer is yes and give explicit examples of such “orbit-blocking” words. Then we use them to give an algorithm that decides whether a fixed word u is automorphic to an input word w in constant (that is, independent of the length of w) average-case time. This is joint work with Lucy Hyde, Eamonn Olive, and Vladimir Shpilrain.
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Afternoon Session I

9) Sanjana Paul (Smith College)
Title: Number Theoretic and Combinatorial Properties of Increasing Sequences of Positive Integers
Abstract: This talk focuses on increasing sequences of positive integers, in particular Complementary Sequences, which are pairs of sequences whose union gives the positive integers and which have no elements in common. Complementary sequences are related to combinatorial games, which are two-player, alternating, deterministic games with perfect information. The objective of the talk is to present some results about complementary sequences, their generation methods and their relationship with combinatorial games, as well as to present some of the research our group has been doing in this area." This is joint work with Amy Pinargote, Almanzo Gao, Eliana Lippa, Emi Neuwalder, and Kanghui Zou, taught by Dr. Geremias Polanco.

10) John T. Saccoman (Seton Hall University)
Title: Spectra of multigraphs that are underlying complete split, Complete split graphs are threshold graphs
Abstract: that have all nodes in the independent set adjacent to all nodes in the clique. In 2002, Hansen et. al. presented criteria for complete split graphs that have integral spectra for their adjacency matrix. We explore spectra of multigraphs that are underlying complete split for some of the matrices associated with graphs. This is joint work with Michael Catli and Joseph Kajon.

11) Abigail Raz (Cooper Union)
Title: The Path Variant of the Explorer-Director Game on Graphs
Abstract: The Explorer Director game, first introduced by Nedev and Muthukrishnan (2008), simulates a Mobile Agent exploring a ring network with an inconsistent global sense of direction. The two players, the Explorer and the Director, jointly control the movement of a token on the graph. During each turn, the Explorer calls any valid distance, d, with the aim of maximizing the number of vertices the token visits, and the Director moves the token to any vertex distance d away with the aim of minimizing the number of visited vertices. The game, on graph G with starting vertex v, ends when no new vertices could be visited assuming both players are playing optimally, and we denote the total number of visited vertices by fd(G,v). Since 2008, many authors have explored fd(G,v) for various graph families as well as analyses of complexity. In this talk, we will focus on a variation of this game focused on path lengths rather than distances. In this variant, if the token is on vertex u, the Explorer is now allowed to select any valid path length, l,  and the Director can now move the token to any vertex v, such that G contains a uv path of length l. The corresponding parameter is denoted by fp(G,v). We will discuss how far apart fd(G,v) and fp(G,v) can be for various graph families. All necessary preliminaries will be discussed - no background in graph theory is assumed. This is joint work with Paddy Yang.

12) Nadia Benakli (New York City College of Technology, CUNY)
Title: Metric Dimension of Generalized Theta Graphs
Abstract:  The metric dimension of a graph, also known as the locating number, is a graph invariant that allows the identification of vertices based on their distances to a selected set of referenc vertices. A generalized theta graph consists of two distinct vertices connected by multiple internally vertex-disjoint paths. These graphs have been investigated in different contexts. When exactly three such paths exist, the graph is simply referred to as a theta graph. Despite their seemingly simple structure, determining the metric dimension of generalized theta graphs has proven to be a challenging problem. In this work, we present new results on the metric dimension of these graphs, revisiting known results, and discuss some conjectures. This is joint work with David Martinez, Nicole Froitzheim.

13) Nhat-Dinh Nguyen (City College of New York, CUNY)
Title: Information Diffusion on Iterated Graphs
Abstract: We explore a particular discrete time process, zero forcing, on graphs which model social networks. The Iterated Local Transitivity ILT model, introduced in 2009 by Bonato et al., models online social networks and captures the notion that friends of friends are likely friends. Later in 2017, Bonato et al. expanded this idea to the Iterated Local Anti-Transitivity ILAT model which captures the notion that enemies of enemies are likely friends. Both the ILT and ILAT models exhibit properties observed in real-world complex networks, such as distances bounded by absolute constants and bad spectral expansion. The zero forcing process, first introduced in 2008 by Barioli et al., is applicable to the minimum rank problem from linear algebra, graph searching algorithms, and determining how fast information can spread in a network\textemdash a natural consideration for graphs modeling social networks. It is defined as follows: Let $S \subseteq V(G)$ where each $v \in S$ is called forced, and each $u \in V(G)\setminus S$ is called unforced. Let $U$ := $V(G)\setminus S$. If $v\in S$ has exactly one neighboring vertex $u \in U$, then $v$ ``forces" $u$, i.e. $u$ is removed from $U$ and added to $S$. If eventually every vertex in our graph is forced, we say our initial set $S$ is a zero forcing set; otherwise, we say $S$ is a failed zero forcing set. The failed zero forcing number, formally introduced by Fetcie et al. in 2015, is the maximum cardinality of any failed zero forcing set. We focus on bounds for the failed zero forcing number of all graphs constructed using the ILT and ILAT frameworks. We obtained these bounds by examining the neighborhoods of finitely many vertices in arbitrary ILT and ILAT graphs. We then made appropriate choices, based on the relationships between specific vertices inherent to these models, of which vertices to include in $S$ such that $S$ would constitute a failed zero forcing set of maximal size. This is joint work with Christopher Brice (Columbia University) and Professor Abigail Raz (The Cooper Union).
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Afternoon Session II

14) Torhira Oshoriameh Aminu (Bowie State University)
Title: Cryptography and Number Theory: Securing Our Digital World
Abstract: This talk will provide an introduction to the role of number theory in modern cryptography, focusing on prime numbers, modular arithmetic, and their application in encryption algorithms such as RSA. We will discuss how number theory is used to ensure the security of digital communications and transactions, from everyday online banking to secure messaging systems. By understanding the mathematical foundations of cryptography, we can appreciate how number theory plays a critical role in protecting privacy and data integrity in the digital age.

15) Lubna Kadhim (Morgan State University)
Title: On the Qualitative Study of an Abstract Fractional Functional Differential Equation via the Ψ-Hilfer Derivative
Abstract:  investigate the existence, uniqueness, Ulam Hyers and generalized Ulam-Hyers stability of the fractional functional differential equation: $$HD^{α,β;Ψ}_0 (u(t) + g(t, u(t))) = Au(t) + f(t, u(t)), t ∈ [0, T], I^{1−γ;Ψ}_0 + u(0) = u_0$$ where $HD^{α,β;Ψ}$ is the Ψ-Hilfer operator. We first establish a variation of constants formula, and then use the Banach fixed point principle and the Krasnoselskii’s fixed point theorem to achieve our existence and uniqueness results. We also explore the stability of this equation under some appropriate conditions. Our results generalize some recent ones on the subject. We finally give an example to illustrate our main result. This is joint work with  Mesfin M. Etefa, and Gaston M. N’Guerekata.

16) Nilava Metya (Rutgers University)
Title: Degrees of the Wasserstein Distance to small toric models
Abstract: The study of the closest point(s) on a statistical model from a given distribution in the probability simplex with respect to a fixed Wasserstein metric gives rise to a polyhedral norm distance optimization problem. One way to measure the ‘complexity’ of the problem is “algebraic complexity”, which is governed by the polar degrees of the Zariski closure of the model. We find the polar degrees of some of these models.

17) Sayantika Mondal (CUNY Graduate Center)
Title: Are these curves the same?
Abstract: The study of extremal lengths of curves and their relations to intersection numbers has a very rich history. In this talk, I look at filling curves on hyperbolic surfaces and consider its length infima in the moduli space of the surface as a type invariant. Then explore the relations between this geometric invariant and a topological namely the self-intersection number of a curve. In particular, for all finite type surface, construct infinite families of filling curves that cannot be distinguished by self-intersection number but via length infimum. Time permitting, I will also discuss some coarse bounds on the metrics associated to these infimum lengths.

18) Emma Dinowitz (CUNY Graduate Center)
Title: Markov partitions for hyperbolic diffeomorphisms
Abstract: We will discuss the construction and application of markov partitions for locally maximal hyperbolic sets for diffeomorphisms. This will be an expository talk.

Organizing Committee:

Siobhan O'Conner, Sandra Kingan, Tamara Kucherenko, Sayantika Mondal (chair), Christian Wolf.

Contact:

If you have any questions about the conference other than funding please email skingan@brooklyn.cuny.edu

Please email gc.women.and.math.conference@gmail.com for all matters related to funding.

Sponsored by the Graduate Center's Mathematics Department and the GC AWM Student Chapter.