CMU Mathematics Department Colloquia

2022 -- 2023

Organizer

• Department of Mathematics Colloquium Coordinator C-Y. Jean Chan

• Because there might be a time delay in updating the webpage, please always check with the Coordinator for the available dates.

Meeting Times and Platforms

Typical Colloquium Talks are Thursday, 4:00–4:50pm, in person, virtual, or HyFlex format. Media is indicated under Remark.
The following table gives the information for all colloquium activities, and each Thursday event, including Department-wise Meetings (3:30pm).
This table includes also courtesy bookkeeping for Tuesday, if any, department-wise meetings (3:30pm).
For Graduate Student Seminar (GSS) schedule on Tuesdays, please click here.

SCHEDULE

Abstracts

Speaker: Kristi Wood (September 22, 2022)
Title: Curricular Training
Abstract: Kristi Wood, Associate Director/Curricular Process & Systems in CIS, will give our department training on the new Curriculm Strategy system for the curricular workflow. (That is, the system that replaces the old green/blue/pink forms.) This system is needed to do MCS updates/changes, etc.

Speaker: Laura Scull (September 29, 2022)
Title: Homotopy Theory for Graphs
Abstract: Homotopy theory studies deformations of geometric objects, an inherently continuous concept. In this talk, we will explore how this translates to the discrete category of graphs. We will see how we can use a little category theory to define a notion of homotopy for graphs, creating an analogous concept of discrete deformations. We will explore the properties of these deformations by looking at the 'fundamental group' of the graph created from homotopy classes of walks. No prior knowledge of either homotopy theory or graph theory will be needed, and many examples and pictures will be given. Parts of this work are joint with Dr. Tien Chih, and parts were developed in collaboration with Fort Lewis College undergraduate students as part of a CURM funded research project.

Speaker: Dmitry Zakharov (October 4, 2022)
Title: Tropical Jacobians and Prym varieties
Abstract: The aim of tropical algebraic geometry is to find polyhedral, piecewise-linear analogues of algebro-geometric objects. The tropical analogue of an algebraic curve is a metric graph. The Jacobian of a metric graph is a real torus that records the intersection numbers of the cycles on the graph.
I will talk about the tropical version of an important construction in algebraic geometry: the tropical Prym variety of a double cover of metric graphs. This is a real torus that records those cycles on the source graph that vanish on the target graph. I will derive a formula for the volume of the Prym variety. I will also describe the tropical version of a classical algebraic construction, the trigonal construction of Recillas.
This is joint work with Yoav Len and Felix Roehrle.

Speaker: Faculty of Mathematics (October 13, 2022)
Title: Fall23--Spring24 Graduate Courses Exhibition
Abstract: In this exhibition, some of the Faculty members who plan to teach elective graduate courses ​including MTH 534, MTH 633, MTH 634, MTH 643, MTH 725 and MTH 737 will give a short presentation about the topics to be covered in the course. It is an opportunity for students to sample the course materials and ask questions to the instructors before they submit Graduate Student Survey Form on Friday, Oct 21, 2022. Pizza will be provided during the presentation. All graduate students and faculty are welcome!

Speaker: Tom Richmond (November 3, 2022)
Title: Topology and Order
Abstract: Several connections between topology and order will be presented. We show that every topology on a finite set X is characterized by an equivalence relation on X and a partial order on the equivalence classes. After several examples, we use this link to count the number of nested topologies on a finite set. We briefly introduce complementation in the lattice of topologies on a finite set and give an algorithm to generate complements for a totally ordered convex topological space.

Speaker: Feryal Alayont (March 2, 2023)
Title: Edge Covers of Graphs: The Story of Building an Accessible and Inclusive Undergraduate Research Project
Abstract: An edge cover of a graph is a subset of the edges so that each vertex is an endpoint for at least one edge. Edge covers provide new combinatorial interpretations to certain number sequences. For example, the number of edge covers of path graphs form the Fibonacci sequence. In summer 2022, five students and I investigated similar sequence patterns in other graph families. I will describe our mathematical results about edge covers of various graph families along with the unusual logistical set-up of this project that allowed for a diverse group of students to participate in undergraduate research. Successes and challenges of this approach will be discussed.

Speaker: Debraj Chakrabarti (April 6, 2023)
Title: Mathematical Conversations With ChatGPT
Abstract: ChatGPT, the recently developed "large language model", has been making headlines. ChatGPT responds to questions posed by users in a startlingly human-like manner, based on a statistical algorithm. Among its latest exploits is to pass the US Uniform Bar Examination with a score in the 90th percentile. There are legitimate fears about the possible impact of these technologies, for example on office jobs that can be potentially replaced by a chatbot.
What will be the impact of AI technologies on mathematics and the mathematical profession? It is too early to reach a definite conclusion, but not too early to be worried. In this open-ended presentation, we will ask ChatGPT simple mathematical and logical questions to try to gauge its mathematical capabilities and try to see if there is any reason to worry about our jobs.

Speaker: Joel Villatoro (April 18, 2023)
Title: A diffeological Approach to Integrating Infinite Dimensional Lie Algebras
Abstract: Lie groups and Lie algebras are mathematical objects commonly used as models for studying symmetry in geometry. Given a Lie group, one can always construct an associated Lie algebra through a process known as "differentiation." The reverse procedure is called integration. For finite-dimensional cases, it is well-established that every Lie algebra arises as the derivative of some Lie group, meaning that every finite-dimensional Lie algebra is integrable. However, this is not always true for infinite-dimensional cases. One particularly interesting class of infinite-dimensional Lie algebras comes from Lie algebroids. In this talk, we will provide an overview of the history of integrating Lie algebroids and the challenges encountered. We will then explore how diffeologies might help us overcome some of these issues.

Speaker: Rachel Domagalski (April 20, 2023)
Title: You've got a friend in me! Or do you? Using Backbones of Bipartite Projections to Unveil Social Networks
Abstract: Signed networks are difficult to collect. Individuals often don't want to report their negative relationships, and occasionally researchers are prohibited from asking about them. One solution is to infer true relationships from bipartite data. Bipartite projections are used in a wide range of network contexts including politics (bill co-sponsorship), geography (firm co-location), genetics (gene co-expression), economics (executive board co-membership), and innovation (patent co-authorship). However, because bipartite projections are always weighted graphs, which are inherently challenging to analyze and visualize, it is often useful to examine the 'backbone', an unweighted subgraph containing only the most significant edges. We'll discuss different methods of backbone extraction, the distributions behind these methods, and their applications to real-world scenarios.

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Past Department Colloquia: Spring 2022/Fall 2021 Spring 2020/Fall 2019 Spring 2019 Fall 2018 Spring 2018 Fall 2017 Spring 2017 Fall 2016

Look for Colloquia Archives for past activities