researchseminars.org

Edmund Harriss (University of Arkansas)
2024-06-28 15:30 - 16:30 UTC | https://researchseminars.org/talk/CompMath/1/
Title: Mappings between abstract and physical spaces (https://researchseminars.org/talk/CompMath/1/)
by Edmund Harriss (University of Arkansas) as part of Relatorium seminar

Abstract
I work as a mathematician and artist, and within the Illustrating Mathematics group, at the heart of this work lie ideas about translation and mapping between physical and abstract spaces, in different ways to just modelling. In particular thinking about ideas in art and mathematical illustration where physical spaces are being used to understand the abstract world (rather than science that normally goes the other way). Images, models and experiences can reveal aspects of the abstract that we do not yet understand and thus drive research. I will introduce some ideas about this and then open the question of how category theory might be useful to understanding the mapping and conversion that is happening between the abstract and the physical and thus how it can be validated and potentially checked for errors.

The talk will be moderated by Namista Tabassum who joined our comp math group recently. Namista is an interdisciplinary researcher and business advisor who has worked with diverse organizations in Canada and Bangladesh, notably leading research projects and facilitating social impact events. Her interest in mathematics and science communication stems from her belief in compassionate mathematics, bridging her passion for art and logic to make complex concepts accessible and engaging.

Irfan Alam (U. Pennsylvania)
2024-05-31 16:00 - 17:00 | https://researchseminars.org/talk/CompMath/2/
Title: How will mathematics education change with the rise of A.I. tutors? (https://researchseminars.org/talk/CompMath/2/)
by Irfan Alam (U. Pennsylvania) as part of Relatorium seminar

Abstract
I have been advising two students, Tomas Nepala and Tunga Bayrak, who have created MotionShark, which is a software that generates video explanations of mathematical problems. This type of technology prompts significant questions about the future role of mathematics educators and the evolution of teaching methods.

After Tomas and Tunga exhibit the current capabilities of their evolving technology, I will give a presentation on some challenges that I think the mathematics education community must brace itself for in the wake of this type of technology. Navigating such challenges requires an active input of mathematicians and this talk is meant to start that conversation at an international level. I will share my vision on how to integrate this type of technology into lower-level mathematics classes in healthy ways, and how I see the scope of such classes adapting and evolving in a future where I argue the context of mathematics will become more important to teach than actual methods of problem solving.

My goal is to start this conversation that will hopefully keep going offline after the talk has ended, since we as a community ought to better understand in a timely manner the directions in which mathematics education will change in the wake of this and similar technologies in near future.
The talk will be moderated by Daniel Filonik who is a postdoc at Carnegie Mellon University (CMU) and foreign guest researcher at the National Institute of Standards and Technology (NIST). Daniel specializes in data visualization and human computer interaction. His current work is focused on natural interfaces for interactive data modeling and analysis with formal foundations in category theory.

Niels Voorneveld (Cybernetica)
2024-04-25 16:00 - 17:00 | https://researchseminars.org/talk/CompMath/3/
Title: Relational Molecules: Using games to interact with formal structures (https://researchseminars.org/talk/CompMath/3/)
by Niels Voorneveld (Cybernetica) as part of Relatorium seminar

Abstract
I love video games, and I love mathematics. For the longest time, I saw them as separate. But as time went on, I realized their similarities: both define worlds besides our own which we can explore and interact with. Combined, games can give a powerful tool to learn about and play with mathematical structures in a non-standard way. In this talk, we look at an idea I have been thinking about in the past few months, that of the search for relational molecules. These are relations which look like and share symmetries with molecules, and are inspired by the works of 19th century philosopher Peirce. We look at examples of such molecules, where they may turn up, and see how a simple game allows people to interact with them to learn their behavior. After the talk, we will have an open discussion about the ideas covered.

David Spivak (Topos Institute)
2024-08-02 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/4/
Title: How the Yoneda lemma applies (https://researchseminars.org/talk/CompMath/4/)
by David Spivak (Topos Institute) as part of Relatorium seminar

Abstract
What is the relationship between your web of concepts about the world and all the examples you've seen of these concepts? And what is the relationship between a generic flower and all the particular flowers or a generic bicycle and all the particular bicycles? A formal answer to this was given by Nobuo Yoneda in a private letter to a founder of Category Theory, Saunders Mac Lane, and this answer has become the most fundamental concept in category theory: the Yoneda lemma.

In this talk, I'll begin by explaining schemas and instances—concept-webs and the system of examples that live in them—in terms of categories C and set-valued functors F:C-->Set. Then I'll explain how each concept (each node in the web) determines a generic instance: the generic flower, the generic bicycle, etc.

So given a concept, how is the generic instance of it related to all the other examples of it? The answer is that the generic instance of flower can be overlaid perfectly onto any particular flower, and all its generic features will be given particular values. This is the content of the Yoneda lemma: given any schema C and functor (system of examples) F: C-->Set, the Yoneda lemma says that "applying F to concept c", i.e. the set of c-examples, is the same as the set of all ways that the generic instance for c can be overlaid onto the system of examples. And this is how the Yoneda lemma "applies"!

Nathan Haydon
2024-08-30 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/5/
Title: Peirce's Existential Graphs and String Diagrams for First-Order Logic (https://researchseminars.org/talk/CompMath/5/)
by Nathan Haydon as part of Relatorium seminar

Abstract
The Existential Graphs are the result of C.S. Peirce's studies in the logic of relations and his concern for developing a better logical notation. In this talk I give an accessible introduction to Peirce's graphs that emphasizes the intuitions behind these notational choices and the resulting inference rules. Along the way I discuss how Peirce's work has been the inspiration for recent advances in categorical logic and show examples of how the graphs help us present and clarify some of our logical concepts.

Priyaa Varshinee Srinivasan (Tallinn University of Technology)
2024-10-04 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/6/
Title: Communicating relational thinking (https://researchseminars.org/talk/CompMath/6/)
by Priyaa Varshinee Srinivasan (Tallinn University of Technology) as part of Relatorium seminar

Abstract
I love math, I love people and I am interested in how they both interact. While being a postdoctoral fellow at the Topos Institute, a team of four including me published an online illustrated live-book on category theory -- which we termed as relational thinking for the purposes of this book -- intended for a general STEM-oriented audience. We used story-telling and leaned in on technology instead of formal symbols to communicate category theory.

In this talk, I will outline the storyline of this book and also touch on the technology that made this book happen. This project is joint work with Paul Dancstep, Brendan Fong, Angeline Aguinaldo, Evan Patterson and many others behind the scenes.

The book is available at https://toposinstitute.github.io/RelationalThinking-Book/cover.html

Karen Little
2024-11-29 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/7/
Title: Exploring the math of awesome reversible knitting (https://researchseminars.org/talk/CompMath/7/)
by Karen Little as part of Relatorium seminar

Abstract
I am an enthusiastic mathematician specializing in reversible knitting which is a branch of knitting focussed on creating fabric that looks beautiful on both sides. This talk will explore concepts, definitions and axioms of reversible knitting. We will start with the two fundamental knitting stitches, venture into duality, symmetry, tiling and transformations and end with the “reversiblest” stitch pattern known, all in a Knitting Relatorium!

Although no physical knitting experience is required or provided, I will supplement the talk with a selection of knitted fabrics as examples of each concept.

Ted Theodosopoulos (Nueva School)
2024-10-25 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/8/
Title: Compassion as Composition (https://researchseminars.org/talk/CompMath/8/)
by Ted Theodosopoulos (Nueva School) as part of Relatorium seminar

Abstract
We propose that categorical notions can be wielded to facilitate the “Yes, and…” experience as a tool for collaborative sense making, as we explore mathematical ideas and communicate our insights. Far from forbiddingly remote abstractions, categorical notions ground our emerging sense of unfamiliar terrains in relational thinking, which interacts constructively with the narratives that populate our mental universe. In this talk we will grapple with ambiguity and co-create mutually reinforcing stories that carry meaning. The resulting experiences help situate mathematical ideas beyond the largely contingent symbols we use to express them.

Daniel Fiłonik
2024-12-27 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/9/
Title: Hypercomplex Numbers: How I stopped worrying and learned to love multilinear algebra (Part 1/2) (https://researchseminars.org/talk/CompMath/9/)
by Daniel Fiłonik as part of Relatorium seminar

Abstract
This seminar will serve up a smorgasbord of ideas revolving around the notion of hypercomplex numbers. Traditionally, the term hypercomplex number refers to an element of a finite-dimensional unital algebra over the field of real numbers. The hypercomplex numbers are stepping stones to learning about Lie groups and group representation theory.

My aim is to reframe some of the key underlying ideas in more modern mathematical language by using multilinear algebra and string diagrams as graphical notation, while simultaneously keeping intact the original intuition of generalizing complex numbers. Ultimately, I hope to motivate further exploration by showing several practical applications of hypercomplex numbers in computer graphics and data visualization.

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The talk will be moderated by Edmund Harriss. Edmund Harriss is a mathematician, artist, and assistant professor at the University of Arkansas. He is the discoverer of the Harriss spiral and the creator of the construction toy Curvahedra. He is the coauthor of Hello Numbers, What Can You Do? and the coauthor and illustrator of two mathematical coloring books: Patterns of the Universe and Visions of the Universe.

Daniel Fiłonik
2025-01-17 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/10/
Title: Hypercomplex numbers: How I stopped worrying and learned to love multilinear algebra (Part 2/2) (https://researchseminars.org/talk/CompMath/10/)
by Daniel Fiłonik as part of Relatorium seminar

Abstract
This seminar will serve up a smorgasbord of ideas revolving around the notion of hypercomplex numbers. Traditionally, the term hypercomplex number refers to an element of a finite-dimensional unital algebra over the field of real numbers. The hypercomplex numbers are stepping stones to learning about Lie groups and group representation theory.

My aim is to reframe some of the key underlying ideas in more modern mathematical language by using multilinear algebra and string diagrams as graphical notation, while simultaneously keeping intact the original intuition of generalizing complex numbers. Ultimately, I hope to motivate further exploration by showing several practical applications of hypercomplex numbers in computer graphics and data visualization.

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The talk will be moderated by Ted Theodosopoulous. Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level fifteen years ago, the last seven at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Matt Insall (Missouri University of Science and Technology)
2025-02-28 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/11/
Title: Non-standard Methods and Universal Algebra (https://researchseminars.org/talk/CompMath/11/)
by Matt Insall (Missouri University of Science and Technology) as part of Relatorium seminar

Abstract
The subject of Universal Algebra (aka General Algebra) has at its core a class of structures called “Algebras”. An algebra can be thought of as a universe of discourse for a computer or calculator that “runs” deterministic code, because calculations in an algebra use functions (in the mathematical sense, no input has multiple outputs). Algebras can be organized into various types or “kinds”, according to a formal language that uses only universally quantified equations. The algebras form a kind of “semantic playground” for mathematicians, and the equations can be thought of as a “syntactic grammar” for establishing “rules of games” for any given section of the playground. At a higher level, one may study the relations and interactions between the rules (syntax) and the algebras (semantics), and classes of algebras with certain desirable properties. Some of the games use finite algebras as their section of the playground but others use infinite algebras. The study of infinite algebras can in some nice ways benefit from knowledge about finite algebras. The goal of this discussion will be to see how Nonstandard Methods can be used to create new concepts in universal algebra, mostly by “playing” in two (generic) “playground sections”. One section is loosely called “the standard world”, and the other is “the nonstandard world”. Finite algebras we consider in the standard world are also finite algebras in the nonstandard world, but some of the algebras viewed as “finite” in the nonstandard world are extensions of infinite algebras in the standard world, so that from the standard perspective, some “nonstandardly finite” or “hyperfinite” algebras are infinite. Results known about finite algebras in the standard world carry over to results about hyperfinite algebras, and can be used then to draw conclusions about the standard algebras they extend. For example,

A standard algebra is locally finite (each of its finitely generated subalgebras is finite) if and only if it has a hyperfinite extension.

Other properties of algebras (other than the property of being finite) in the standard world have nonstandard analogues as well, and we can use this general framework to “create” new properties of algebras in the standard world. Hopefully, with audience participation, we will be able to create such a property that is new (to us, at least).

References:

Hurd, Albert E.; Loeb, Peter A. An introduction to nonstandard real analysis. Pure and Applied Mathematics, 118. Academic Press, Inc., Orlando, FL, 1985.

Stanley N. Burris, Stanley N.; H.P. Sankappanavar, H. P. A Course in Universal Algebra, https://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html

Insall, M. (1991), Nonstandard Methods and Finiteness Conditions in Algebra. Mathematical Logic Quarterly, 37: 525-532. https://doi.org/10.1002/malq.19910373303

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The talk will be moderated by Irfan Alam. Irfan is a mathematician, abstract artist, and aspiring philosopher. He currently works as a postdoctoral fellow in the department of Computer and Mathematical Sciences at University of Toronto Scarborough. Irfan’s research background is in the area of nonstandard analysis, especially in its applications to other areas of mathematics such as probability theory and topology.

Matt Insall studied chemical engineering (BS, 1986) and mathematics (BS, 1985) at University of Houston, doing a MS (1987) and PhD (1989) with Professor Klaus Kaiser, also at University of Houston. He taught mathematics in Rolla, Missouri, at Missouri University of Science and Technology (S&T) from 1989 to 2024 and has now retired. He and his wife have four children, two step grandsons, two grandsons, and two granddaughters. Dr. Insall’s research career has included solo and collaborative projects in mathematics and its applications, mainly with colleagues in various departments at S&T. He is currently on a courtesy appointment in the S&T mathematics and statistics department, finishing work with PhD students. In retirement he is continuing to learn mathematics and its applications, following some current events, continuing some writing projects in mathematics, and enjoying meeting new people over coffee or online, to discuss mathematics and education and science.

Rem (Simuli, Inc.)
2025-03-28 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/12/
Title: Deconstructivist Mathematics (https://researchseminars.org/talk/CompMath/12/)
by Rem (Simuli, Inc.) as part of Relatorium seminar

Abstract
I work as a mathematical developer and are currently interested in fully relational models of computations.

In this talk, we will explore the relationship between mathematical intuition and formal rigor, delving into the philosophical and structural foundations of mathematics. The main aim is to examine the process of formalizing mathematical intuitions, highlighting how this process can itself be formalized within a mathematical framework. The layers of abstraction offered by Category Theory mirror the progression from computational to conceptual reasoning. We start from apparent dichotomies appearing in diverse fields of knowledge, such as axiomatic versus structural foundations of mathematics. We then go over the impact and implications of the crisis of foundations, the role of circularity in mathematical reasoning, and the importance of fostering alternative approaches to learning and teaching mathematics. Through allegories, metaphors, and analogies, we illustrate how mathematical concepts can be represented and understood in different contexts, emphasizing the interconnectedness of mathematical ideas. We conclude by advocating for a holistic view of mathematics, one that transcends traditional dichotomies and embraces the dynamic, evolving nature of mathematical thought.

This talk is aimed at both mathematicians and philosophers, offering a deep dive into the structural and philosophical underpinnings of mathematics, while also providing practical insights into the development and teaching of mathematical concepts.

Moderator: The talk will be moderated by Nathan Haydon. Nathan is a philosopher working on methods of reasoning in logic and science. Much of his work is inspired by Charles S. Peirce, including Peirce’s pragmatism and Peirce’s formal developments in diagrammatic logic. Along these lines, Nathan has most recently been working on the logic of string diagrams. Finally, Nathan is also interested in the broader ethical and meta-ethical positions that follow from scientific reasoning.

C.B. Wells
2025-04-25 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/13/
Title: Holdea: Visual Logic Interface (https://researchseminars.org/talk/CompMath/13/)
by C.B. Wells as part of Relatorium seminar

Abstract
There is a simple visualization of logic: relations of types are nodes with ports, equalities are wires connecting ports, conjunction is juxtaposition, negation is wrapping in an opposite color, and entailment is nesting of nodes. This describes the string diagrams of a self-dual cartesian bifibered category, which models a first-order logic.

I'm creating an interface for visual logic - a user connects data, tables become nodes in the canvas, and they can form predicates and rules just by manipulating nodes and wires. It's in the early stage, but the core is established: the visualization generates a prolog query in the side panel, executes, and returns results in the bottom panel. I'll demonstrate, explain some background theory and implementation, and then open discussion.

Moderator: The talk will be moderated by Nathan Haydon. Nathan is a philosopher working on methods of reasoning in logic and science. Much of his work is inspired by Charles S. Peirce, including Peirce’s pragmatism and Peirce’s formal developments in diagrammatic logic. Along these lines, Nathan has most recently been working on the logic of string diagrams. Finally, Nathan is also interested in the broader ethical and meta-ethical positions that follow from scientific reasoning.

Shaowei Lin
2025-05-30 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/14/
Title: Refine yourself a code for great good! (https://researchseminars.org/talk/CompMath/14/)
by Shaowei Lin as part of Relatorium seminar

Abstract
How do you code? Andrej Karpathy who coined the term "vibe coding," says that for professional coding tasks, he picks single concrete incremental changes and, with AI assistance, plans them, executes them, and evaluates them. Refinement is the process of making incremental changes. It is not just the primary way we design and construct code, but also how we repair them and upgrade them, often collaboratively with other coders, designers and users.

The central objects in refinement are partially implemented programs. Partial programs are examples of open systems - each has a formal external specification (e.g. a function type) and an implementation with internal holes which are also formally specified. Partial proofs, such as those manipulated by the proof assistants, are also examples of open systems. Open systems compose by refinement or hole-filling, where a typed hole can only be filled by an open system of the right spec. An open system in some representation can also be translated (transported, projected or lifted) to some open system in another representation. In fact, open systems, with their refinements and translations, form a double category!

In this talk, I hope to share some concrete examples of this refinement-centric approach in formal verification, program synthesis and theorem proving. I believe that this approach can help us to leverage AI assistance in coding, to decentralize and democratize coding, and to build safe, secure and sustainable software systems.

Moderator: The talk will be moderated by Daniel Filonik. Daniel specializes in data visualization and human computer interaction. His recent work focused on natural interfaces for interactive data modeling and analysis with formal foundations in category theory.

Broni Czarnocha and Malgorzata Marciniak (Hostos CC of the City University of New York and LaGuardia CC of the City University of New York)
2025-06-27 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/15/
Title: The interplay between two opposing perspectives on creativity (https://researchseminars.org/talk/CompMath/15/)
by Broni Czarnocha and Malgorzata Marciniak (Hostos CC of the City University of New York and LaGuardia CC of the City University of New York) as part of Relatorium seminar

Abstract
In our presentation, we will explore a dialogue between two somewhat contrasting perspectives on creativity. One speaker will present the concept of Teaching-Research as a manifestation of creative practice, while the other will examine the interplay between the conscious and subconscious mind, highlighting both the boundaries and the connections that shape the creative process.

Broni: Creativity of Mathematics Teaching-Research.
In general, creativity, and especially the creativity of Aha! Moment (called bisociation by Koestler (1964t)) takes a place within two unconnected matrices of thought joined together by the insight. Czarnocha and Baker (2021) abstracted these two matrices to the concept of the bisociative frame, and we used it as the tool to find areas of enhanced creativity within different theories and practices of teaching.
Teaching and research constitute such a frame, taking into account a very meager connection between them, and because of that the creative TR methodology is so promising. The presentation will provide an example of creativity while practicing TR methodology.

Malgorzata: Creativity as a collaboration between conscious and subconscious
In my work, creativity is viewed as a dynamic, cyclical process involving alternating phases of conscious and subconscious activity. This aligns with Graham Wallas’ stages: preparation, incubation, illumination, and reflection, outlined in The Art of Thought (Wallace, 1926). Over time, this cycle mirrors the state of flow described by Mihaly Csikszentmihalyi in Creativity: Flow and the Psychology of Discovery and Invention (1996). Conscious phases involve deliberate effort, analysis, and reflection, while subconscious phases are more elusive, yet crucial. The most intriguing moments occur during spontaneous shifts between phases, when conscious and subconscious processes interact, offering insights that feel both intentional and mysteriously emergent.

This conversation will be moderated by Ted Theodosopoulos. Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Ted Chinburg (University of Pennsylvania)
2025-07-25 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/16/
Title: Long term effects of university teaching practices (https://researchseminars.org/talk/CompMath/16/)
by Ted Chinburg (University of Pennsylvania) as part of Relatorium seminar

Abstract
In this talk I'll discuss some teaching practices that are not popular with students but which can lead to better test scores at the end of a semester. This brings up the question of the long term harm to student motivation produced by such practices. At the end I'll suggest some norms for university departments engaged in debates about teaching.

Moderator: Irfan Alam

Brendan Fong (Topos Institute)
2025-08-29 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/17/
Title: Abstractions for Real People (https://researchseminars.org/talk/CompMath/17/)
by Brendan Fong (Topos Institute) as part of Relatorium seminar

Abstract
Computing is built on abstractions. Abstractions forget details, so that we can focus on what is important. What happens, however, when we forget something of value? I argue that certain risks and fears around AI today result from action informed by abstractions that diverge from what matters in their context of use. Moreover, I suggest that building better societal practices of abstraction is a task to which mathematicians – especially category theorists – are well placed to contribute. To begin a conversation, I envision a practice of abstraction that prizes accessibility, responsiveness, and pluralism. I'll illustrate this practice via ongoing work at Topos, especially our collaborative modelling platform CatColab.

bio: Brendan Fong serves as the founding chief executive of Topos Institute, an international research nonprofit building tools for collective sense-making. He is co-author of textbook An Invitation to Applied Category Theory, serves on the steering committee of the Adjoint School, served as a founding executive editor of the open access journal Compositionality, and co-directed the Inaugural Singapore Conference on AI for the Global Good. He received a DPhil in Computer Science from Oxford, with postdoctoral training at UPenn and MIT.

Moderator bio: The talk will be moderated by Priyaa Varshinee Srinivasan. Priyaa is a postdoctoral fellow at the Tallinn University of Technology, and a former colleague of Brendan (the speaker). She specializes in applied category theory specializing in quantum sciences. Her vision is for everyone to experience the joy of mathematics in their own way.

Danielle Bowerman (Missouri University of Science and Technology)
2025-09-12 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/18/
Title: Extension Monads: Some Structure Theorems (https://researchseminars.org/talk/CompMath/18/)
by Danielle Bowerman (Missouri University of Science and Technology) as part of Relatorium seminar

Abstract
To some extent, this presentation follows the seminar titled "Non-standard Methods and Universal Algebra" by Matt Insall presented back in February. In this presentation, we take algebraic structures---a pair consisting of (1) a set of elements to compute upon and (2) a set of computational instructions, called algebras heretofore---into the nonstandard setting. This process can both enlarge and endense said algebra, often causing new elements to appear both "far away" from and "in between" the elements of the original algebra, while preserving all of the same logical properties of the original.

The additional elements are often clustered around directly mapped elements from the standard (original) setting. In the case of these algebras, we define a third structure, the extension monad, of the elements that are very close to the original algebra. This extension monad is, as a set, in between the standard and nonstandard version of the algebra and while not logically identical, captures the local behavior of the computational instructions, known as operations.

Bio: Danielle Bowerman studied mathematics at Evangel University and earned a bachelor of science in 2019. She then went on to join a mathematics PhD program as a Chancellor's Distinguished Fellow at the Missouri University of Science and Technology and expects her PhD in the fall of 2025. She taught a few sections of College Algebra at some point.

Moderator: This talk will be moderated by Matt Insall. Matt Insall is a mathematician, father of four (two sons and two daughters), and grandfather of four boys and two girls. He’s written poems and a song, and performs occasionally at open mic events. Matt retired in September 2024 from his position in the faculty of the Missouri University of Science and Technology Department of Mathematics and Statistics after 35 years in that position.

Antonio Vassallo (Warsaw University of Technology)
2025-09-26 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/19/
Title: Rethinking Reality without Space and Time (https://researchseminars.org/talk/CompMath/19/)
by Antonio Vassallo (Warsaw University of Technology) as part of Relatorium seminar

Abstract
This talk explores a Leibnizian/Machian perspective on physics in which space, time, and intrinsic properties are not fundamental, but emergent from an underlying web of relations. Drawing on the framework of Pure Shape Dynamics and the metaphysics of self-subsisting structures, I will argue that physical reality can be fully described without appealing to external backgrounds or absolute quantities. Instead, what persists are evolving patterns of relational quantities that together form a coherent, self-contained structure. This shift not only reframes familiar concepts like identity, locality, and entanglement, but also invites us to reconsider the ontological status of temporality itself as a product of internal perspective within an undivided whole.

Speaker bio: Antonio Vassallo is Assistant Professor at the Warsaw University of Technology. His research lies at the intersection of philosophy and fundamental physics, with a focus on relational approaches to space, time, and quantum theory. He holds a MSc in physics from the University of Catania and a PhD in philosophy from the Universities of Lausanne and Warsaw. He has held research positions in Switzerland, Spain, and Poland. Among his publications is the edited volume "The Foundations of Spacetime Physics: Philosophical Perspectives" (Routledge, 2022).

Moderator: This talk is moderated by Ted Theodosopoulos. Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Nick Watters (MIT)
2025-10-17 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/20/
Title: How can we understand the neural basis of thought? (https://researchseminars.org/talk/CompMath/20/)
by Nick Watters (MIT) as part of Relatorium seminar

Abstract
Neuroscience is undergoing a technological revolution, a “Moore’s Law” for neural recording that is allowing us to measure the activity of the brain at ever-increasing resolution. However, simply recording neural activity does not tell us how the brain works. To understand how the brain works, we must construct models that connect neural activity to interpretable principles of thought. This modeling becomes increasingly important as we tackle more abstract, cognitive types of thought that arise from the coordinated activity of large populations of neurons. In this talk, I’ll discuss approaches to modeling such large-scale neural activity. I’ll focus primarily on one cognitive domain: Our ability to predict the kinematics of moving objects. We use this ability regularly in daily life, from catching a ball to crossing a busy street. I’ll present neural data recorded from subjects predicting the kinematics of moving objects, introduce a modeling paradigm for interpreting this data, and discuss the implications of the neural latent variables this modeling effort reveals. I’ll conclude by sharing an optimistic outlook on the future of systems neuroscience and speculation about potential implications for artificial intelligence.

Speaker bio: Nick Watters is a postdoctoral associate at MIT studying the neural basis of cognition and motor control in the Jazayeri lab, where he was a PhD student beforehand. Prior to joining MIT, he worked at Google DeepMind as a research engineer, studying unsupervised visual structure-learning and sample-efficient reinforcement learning. Prior to joining DeepMind, he was an undergraduate at Harvard studying math, computer science, and neurobiology.

Moderator: This talk is moderated by Ted Theodosopoulos. Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Theo McKenzie (Stanford University)
2025-10-31 15:30 - 16:30 | https://researchseminars.org/talk/CompMath/21/
Title: The Quantum Chaos of Real-World Networks (https://researchseminars.org/talk/CompMath/21/)
by Theo McKenzie (Stanford University) as part of Relatorium seminar

Abstract
Modern science increasingly relies on predictions derived from massive, interconnected data sets—from social networks to neural activity to the internet. To understand these complex systems, we must move beyond surface-level correlations and uncover the fundamental principles that govern their structure and dynamics. Surprisingly, a fruitful way to analyze these networks is to use the framework created to study atoms in quantum systems. In this talk, I will discuss recent progress in analyzing large networks through the lens of spectral graph theory and quantum chaos. This perspective reveals deep connections between randomness, geometry, and statistical physics, allowing us to prove sharp results about the universal behavior of large networks. I’ll trace the development of these ideas from classical spectral graph theory to modern advances inspired by quantum chaotic systems, and highlight how these methods provide new tools for distinguishing order from noise in complex data. I’ll conclude by discussing open questions and emerging directions at the intersection of network science, probability, and mathematical physics.

Speaker bio: Theo McKenzie is a postdoctoral fellow at Stanford University studying probability theory through the lens of random graphs. Specifically, he studies the relationship between the spectral geometry of graphs and quantum chaos. Previously, he was a PhD student at Berkeley and a postdoctoral fellow at Harvard.

Moderator: This talk is moderated by Ted Theodosopoulus. Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Bob Coecke (University of Oxford)
2025-11-14 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/22/
Title: Kindergarten Quantum Mechanics, now for real! (https://researchseminars.org/talk/CompMath/22/)
by Bob Coecke (University of Oxford) as part of Relatorium seminar

Abstract
Over some 20 years we have developed a diagrammatic quantum formalism, sometimes referred to as quantum picturalism, or categorical quantum mechanics. We have written two books on it [2, 3]. This project was in part initiated in a talk some 20 years ago, with the title Kindergarten Quantum Mechanics [1]. Two things have happened since:

(1) We showed that this formalism enabled secondary school students to perform exceptionally well on an Oxford University post-grad quantum exam, as reported in The Guardian/Observer [4]. Almost 50% of the students obtained a distinction, and 80% passed [5]. Those numbers are better than typical Oxford University MSc students. In Greece quantum picturalism is already used to teach quantum at secondary school level, and several other countries are in the process of doing so too.

(2) John von Neumann himself who denounced `his own’ quantum formalism, that relies on Hilbert space. Alternatives had been proposed, including by von Neumann himself, but none play a role in quantum theory today. On the other hand, quantum picturalism is now widespread in quantum industry, with applications including circuit optimisation and error-correction, with Peter Shor among the proponents. The formalism is also used as the basis for interpretable AI, and even music [6].

Hence quantum picturalism has succeeded in providing an alternative formalism for quantum, with several advantages over the usual formalism, be it as an educational tool, an engineering tool, or a vehicle to explore applications in new areas.

[1] Bob Coecke (2006) Kindergarten quantum mechanics. Quantum Theory: Reconstructions of the Foundations III. AIP Conference Proceedings. Vol. 810. No. 1. American Institute of Physics.

[2] Bob Coecke & Aleks Kissinger (2017) Picturing Quantum Processes. Cambridge University Press.

[3] Bob Coecke & Stefano Gogioso (2022) Quantum in Pictures. Quantinuum.

[4]https://www.theguardian.com/science/2023/dec/16/physicist-bob-coecke-its-easier-to-convince-kids-than-adults-about-quantum-mechanics

[5] Selma Dündar-Coecke, Caterina Puca, Lia Yeh, Hamza Waseem, Emmanuel Pothos, Thomas Cervoni, Sieglinde M-L. Pfaendler, Vincent Wang-Maścianica, Peter Sigrist, Ferdi Tomassini, Vincent Anandraj, Ilyas Khan, Stefano Gogioso, Aleks Kissinger, & Bob Coecke (2025). Making the quantum world accessible to young learners through Quantum Picturalism: An experimental study. arXiv preprint arXiv:2504.01013.

[6] https://www.youtube.com/watch?v=-7q7n8TYPdo

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Speaker Bio: Professor Coecke is a theoretical physicist and logician, and a former Chief Scientist at Quantinuum, leading its Quantum-Compositional Intelligence (QCI) research team. He is also Distinguished Visiting Research Chair at Perimeter Institute for Theoretical Physics, Emeritus Professor at Wolfson College, Oxford University, and a Visiting Fellow at the Computer Science Department and the Mathematical Institute of Oxford University.

He is a founding father of the QPL (Quantum Physics and Logic) and ACT (Applied Category Theory) communities, of the diamond-open-access journal Compositionality, and Cambridge University Press' Applied Category Theory book series.

He is best known for pioneering a simple, picture-based approach to quantum mechanics—sometimes called “Kindergarten Quantum Mechanics”—that allows anyone to grasp quantum ideas with no formal background in mathematics.

https://www.cs.ox.ac.uk/people/bob.coecke/

Bob Coecke

Wolfson College Oxford, Perimeter Institute

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Moderator: The talk will be moderated by Priyaa Varshinee Srinivasan. Priyaa is a postdoctoral fellow at the Tallinn University of Technology researching categorical quantum mechanics. Her vision is for everyone to experience the joy of mathematics in their own way. She has co-authored a live digital book titled “Relational thinking: from abstractions to applications” which reveals the thought-process behind creating mathematics (category theory) using story-telling, illustrations, and visualization of computations. The material is available at https://toposinstitute.github.io/RelationalThinking-Book/cover.html.

Pawel Sobocinski (Tallinn University of Technology)
2025-11-28 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/23/
Title: How I fell in love with string diagrams (https://researchseminars.org/talk/CompMath/23/)
by Pawel Sobocinski (Tallinn University of Technology) as part of Relatorium seminar

Abstract
I will talk about a research adventure I had 10 years ago, rediscovering linear algebra with string diagrams, and resulting in the blog Graphical Linear Algebra and the paper Interacting Hopf Algebras in collaboration with Filippo Bonchi and Fabio Zanasi. This was followed by several subsequent papers and PhD theses that developed the theory further. But more importantly than blogs and papers, it was one of the most fun experiences that I’ve had with research. Along the way I discovered some fun little mathematical facts, some of which I’ll share in this talk.

Speaker Bio: Pawel Sobocinski is Professor of Trustworthy Software Technologies at the Tallinn University of Technology. He leads the Laboratory for Compositional Systems and Methods. He takes part in CHESS, the Cyber-security Excellence Hub in Estonia and South Moravia, funded by the European Commission. He is also a TalTech PI of EXAI, the Estonian Centre of Excellence in Artificial Intelligence, financed by the Estonian Ministry of Education and Research. He is also the author of the blog series on Graphical Linear Algebra (linear algebra through string diagrams) --- https://graphicallinearalgebra.net/.

Moderator: The talk will be moderated by Priyaa Varshinee Srinivasan. Priyaa is a postdoctoral fellow at the Tallinn University of Technology researching categorical quantum mechanics. Her vision is for everyone to experience the joy of mathematics in their own way. She has co-authored a live digital book titled “Relational thinking: from abstractions to applications” which reveals the thought-process behind creating mathematics (category theory) using story-telling, illustrations, and visualization of computations. The book can be found at https://toposinstitute.github.io/RelationalThinking-Book/cover.html.

David Stern (IDEMS International)
2025-12-12 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/24/
Title: Impact Activating Mathematics (https://researchseminars.org/talk/CompMath/24/)
by David Stern (IDEMS International) as part of Relatorium seminar

Abstract
This talk will discuss experiences of Mathematicians who have immersed themselves in supporting positive social impact. Concrete examples will be given which highlight the value of being present in the room, listening and adding value with basic skills. It will also present how taking such a service approach can surprisingly lead to abstractions which pose questions which seem categorical in nature.

The talk will also highlight the value of a collaborative service approach, when working as a transdisciplinary mathematician, which is often in opposition with competitive nature of Mathematics in our education systems. This observation will lead to a discussion about whether there is a different approach to education in the Mathematical Sciences which could transform societal perceptions.

Speaker bio: David is a mathematical scientist who holds a PhD in Algebraic Geometry. David spent his formative years in Niger, where he was exposed to the generosity of families and the power of community best practices and networks for those in extreme poverty.

David worked in business, writing software for banks, before tuning to a career in social impact. He embedded in a Kenyan university as a lecturer on a local salary. There he experienced first-hand the innumerable inequalities faced by talented individuals in low-resource environments.

In this African context, David first turned his mathematical skills to impact innovation to support digital and data inclusion in underserved environments and developed the collaborative innovation best practices that underpin IDEMS.

Moderator: This talk is moderated by Ted Theodosopoulus. Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

The Relatorium Group
2026-01-16 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/25/
Title: Looking back at 2025 (https://researchseminars.org/talk/CompMath/25/)
by The Relatorium Group as part of Relatorium seminar

Abstract
After a rich second year of Relatoria, and on the heels of a third successful in-person session, at the recent Joint Mathematics Meetings in Washington, DC, we are taking a look back at 2025 in our first Open Mic event. We invited our speakers back, to join us for a conversation about the lessons of compassionate mathematics. What have we learned collectively from the Relatorium experience? What themes emerge as connecting principles across the talks? How are the success and challenges of the year guiding our hopes for the future?

Speakers: The Relatorium Group

The Relatorium Group is a collective of more than a dozen researchers and practitioners in mathematics, computer science and philosophy from around the world. We have been exploring innovative modalities for communicating, teaching and learning mathematics. Our approach uses tools inspired from Applied Category Theory (ACT), which focuses broadly on the relational aspects of mathematics. We seek to leverage computational environments organized around principles of compositionality to support the perspectives of the learner in mathematical experiences.

Mike Titelbaum
2026-01-30 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/26/
Title: Topological obstacles to shared priors (https://researchseminars.org/talk/CompMath/26/)
by Mike Titelbaum as part of Relatorium seminar

Abstract
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on the full space? This formulation of the consistency problem for conditional probabilities is significant in Bayesian epistemology and probabilistic reasoning, as it describes the conditions under which a collection of agents can reach agreement by sharing information. We derive a necessary and sufficient condition under which joint compatibility is equivalent to pairwise compatibility. This condition is stated in terms of the cohomology of a simplicial complex constructed from the given probability measures, exposing a novel application of algebraic topology to Bayesian reasoning.

Speaker Bio: Michael G. Titelbaum is a Vilas Distinguished Achievement Professor in the Department of Philosophy at the University of Wisconsin-Madison. He has published Quitting Certainties and Fundamentals of Bayesian Epistemology, both with Oxford University Press. He received a PhD in Philosophy from the University of California, Berkeley in 2008. Before doing that, he was a high school math teacher for four years.

Moderator: Ted Theodosopoulos.
Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Gabriele Carcassi (University of Michigan)
2026-02-13 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/27/
Title: Open problems in Physical Mathematics (https://researchseminars.org/talk/CompMath/27/)
by Gabriele Carcassi (University of Michigan) as part of Relatorium seminar

Abstract
Part of our larger Assumptions of Physics research program, the aim of Physical Mathematics is to develop a set of basic mathematical starting points with a clear and tight physical justification that can serve as a foundation for all physical theories. The idea is to have a shared notion of states and processes that can generalize features and theorems common to all physical theories, while finding the specific ones through addition of further physical assumptions. We will give a short overview of the approach and then focus on open problems and mathematical conjectures to foster discussion. In particular, we will see how a physical theory must at least provide a space of ensembles that must have a T_0 second countable topology, a convex structure and an entropy. We will see how we can already show that the interplay between this structure constrains the space, leading to constructions that find connection to many areas (e.g. measure theory, Choquet theory, information geometry, orthogonality spaces, quantum logic, ...) and we conjecture whether these axioms can already show that an ensemble space is a bounded subset of a locally convex metrizable topological vector space, or further conditions must be found.

Speaker bio:
Gabriele Carcassi is a researcher in the physics department of the University of Michigan. Together with prof. Christine A. Aidala, he leads a research program called Assumptions of Physics ( https://assumptionsofphysics.org ) that aims to find a minimum set of physical assumptions from which the laws can be rigorously rederived.

Moderator: Ted Theodosopoulos.
Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Tai-Danae Bradley (SandboxAQ)
2026-02-27 16:30 - 17:30 | https://researchseminars.org/talk/CompMath/28/
Title: What is a good quantum encoding? (https://researchseminars.org/talk/CompMath/28/)
by Tai-Danae Bradley (SandboxAQ) as part of Relatorium seminar

Abstract
One aim of quantum machine learning is to determine whether quantum computers can provide advantages over traditional machine learning. This exploration depends on how classical data is encoded onto a quantum computer, a choice that can vary significantly from one learning task to another. Recent studies have demonstrated that identifying relevant mathematical structures in the data can yield valuable insights into what constitutes a good encoding choice. In this talk, I will introduce these concepts from a high level and explain how viewing them through a category-theoretic lens can offer a general, yet principled, perspective on designing quantum encodings that preserve mathematical structure.

Speaker bio:
Tai-Danae Bradley is a mathematician and creator at SandboxAQ, a startup company focused on AI and quantum technologies, and a visiting research professor of mathematics at The Master’s University. She has a PhD in mathematics from the CUNY Graduate Center and spent time as a postdoctoral researcher at X, The Moonshot Factory (Google X) before joining SandboxAQ. She is the creator of the mathematics blog Math3ma, as well as a coauthor of the graduate-level textbook Topology: A Categorical Approach and a former co-host of the PBS YouTube channel “Infinite Series”. Her research interests include category theory, machine intelligence, and quantum physics.

Moderator: Ted Theodosopoulos
Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Irfan Alam, Daniel Reinholz, Sarah Tillman
2026-03-20 15:30 - 16:45 | https://researchseminars.org/talk/CompMath/29/
Title: Panel on "Neurodiversity in Mathematics" (https://researchseminars.org/talk/CompMath/29/)
by Irfan Alam, Daniel Reinholz, Sarah Tillman as part of Relatorium seminar

Abstract
Several fundamental mathematical discoveries across history were made by mathematicians who would likely identify with some sort of neurodivergence, had they grown up in the present time when our understanding of different neurotypes and associated "invisible" disabilities is more refined and well-understood. While our society does value the numerous scientific contributions of neurodivergent scholars, it has a tendency to do so by putting them on a pedestal, by stereotyping them as something akin to a "mad genius". Learning about historical role models who achieved the highest academic success (for example, Newton, Erdős, etc.) can create a sense of pride in the minds of young aspiring neurodivergent scholars, but it is not realistic to aim to be the next Newton or the next Erdős. From the point of view of disability advocacy within mathematical practice, it is important to create an approach that celebrates neurodiversity without putting it on an unrealistic pedestal. Therefore, on the occasion of Neurodiversity Celebration Week, we bring together a group of neurodivergent mathematicians to share their personal testimonies about how their neurodivergent identities impacted their academic pursuits. Our dialogue aims to celebrate neurodiversity in mathematics, while being mindful about identifying the barriers to entry that many neurodivergent people face, so that we can work toward a vision of future mathematical practice that is more inclusive and less ableist.

Panelists' bios:
Irfan Alam is an autistic mathematician, currently working as a postdoctoral fellow at University of Toronto Scarborough. Irfan’s mathematical focus is on applications of nonstandard analysis to standard mathematics, especially in probability theory, topology, and lately in the foundations of machine learning. He also works on the philosophy of mathematical practice, with particular interests in the history of infinitesimals and in epistemic injustices in mathematics caused by various socio-cultural norms. Since Fall 2022, he has been on the autistic research advisory board of the "Autism in Context" lab at the University of Delaware.

Daniel L. Reinholz is a Professor of Mathematics and Statistics at San Diego State University. Dr. Reinholz engages in transformative research on classroom equity in postsecondary mathematics. This work has been organized around the development of the EQUIP tool, which generates actionable data to illuminate subtle patterns of classroom participation that result in inequities (by race, gender, disability, etc.). These data can be incorporated into robust professional learning opportunities through equity learning communities that support instructors to transform their teaching. As an autistic and multiply disabled academic, Dr. Reinholz is involved in disability organizing, and is a co-founder of "Sines of Disability". Dr. Reinholz has published over 75 refereed journal articles, and is the author of the recent book, "Equitable and Engaging Mathematics Teaching: A Guide to Disrupting Hierarchies in the Classroom". Dr. Reinholz’s second solo-authored book, "Equity Learning Communities", was published by Harvard Education Press in Fall 2025. Dr. Reinholz also has a forthcoming book on disability in the history of mathematics, to be published with 619 Wreath later this year.

Sarah Tillman is a neurodivergent and disabled independent scholar with a master's degree in applied mathematics. Since 2019 she has been on the Autistic research advisory board of the "Autism in Context" lab at the University of Delaware. As part of this work she has co-authored two papers, one published in "Autism" and the other in "Multiple Voices".

Moderator bio: Namista Tabassum (MBA) is a neurodivergent person of colour, and an interdisciplinary researcher with 10+ years of experience working across business research, policy analysis, communications, and operational strategy. She's currently the Labour Market Specialist at WorkLink Employment Society, where she applies cross-sector research to inform evidence-based programs and strategic communication tools. Her work focuses on translating complex data into practical insights that support decision-making in research, community, and organizational contexts.

Dmitri Tymoczko (Princeton University, and Santa Fe Institute)
2026-05-01 15:30 - 16:45 | https://researchseminars.org/talk/CompMath/30/
Title: Music and Symmetry (https://researchseminars.org/talk/CompMath/30/)
by Dmitri Tymoczko (Princeton University, and Santa Fe Institute) as part of Relatorium seminar

Abstract
Almost all music is concerned with three fundamental properties: pulse, pitch, and transformed repetition. Many musical transformations are invertible, and hence generate symmetry groups. Symmetry groups in turn give rise to a rich network of mathematical structures including quotient spaces and the fundamental group. This conceptual network originally appeared in conjunction with continuous spaces, but recent work has shown it to be universal. My talk will outline this universal structure and explore some of its consequences, not just for making and understanding music, but also for thinking about larger philosophical questions.

Speaker's bio:
Dmitri Tymoczko is a composer and theorist who teaches at Princeton university and is affiliated with the Santa Fe Institute.

Moderator's bio:
Ted Theodosopoulos is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Mehrnoosh Sadrzadeh (University College London)
2026-05-22 15:30 - 16:45 | https://researchseminars.org/talk/CompMath/31/
Title: A Quantum Approach to Vision Language Modelling (https://researchseminars.org/talk/CompMath/31/)
by Mehrnoosh Sadrzadeh (University College London) as part of Relatorium seminar

Abstract
Vision-language models excel at large-scale image-text alignment but often neglect the compositional structure of language, leading to failures on tasks that hinge on word order and predicate-argument structure. We show how techniques from tensor networks and variational quantum circuits help us solve the problem. To this end, we introduce two tools DisCoCLIP and QuCLIP, multimodal encoders that combine a frozen CLIP vision transformer with a tensor network text encoder that explicitly encodes syntactic structure. We also work with translations of syntax into variational quantum circuits. We train both models with a self-supervised contrastive loss and show how the models improve on compositional benchmarks such as SVO-Probes and ARO, while using a significantly smaller number of parameters. The parameter reduction is a known feature of tensor networks and variational quantum circuits, and for this case, was on average from hundreds of millions to tens of thousand.

Speaker's bio: Mehrnoosh is a Professor of CS, leads UCL CS's Quantum Learning Labs, and is the CS Director of Research. Her research is supported by a Royal Academy of Engineering (RAEng) Research Chair, jointly with the BBC and Quantinuum Ltd. Mehrnoosh’s UG and MSc studies were in Sharif University in Iran. Her PhD in University of Quebec at Montreal. Previously, Mehrnoosh had two RAEng Industrial Fellowships, in QMUL and UCL, an EPSRC Career Acceleration Fellowship in Oxford, an EPSRS PDRF and a Wolfson College Junior Research Fellowship, also at Oxford.

Moderator's bio: Ted Theodosopoulos is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Bartłomiej Skowron and Jarosław Chudziak (Warsaw University of Technology)
2026-06-19 15:30 - 16:45 | https://researchseminars.org/talk/CompMath/32/
Title: Virtue, Vice, and Socratic Irony: Benevolent LLMs as Tools for Moral Enhancement (https://researchseminars.org/talk/CompMath/32/)
by Bartłomiej Skowron and Jarosław Chudziak (Warsaw University of Technology) as part of Relatorium seminar

Abstract
As part of the concept of a benevolent multi-agent AI, we propose introducing "benevolent" and "malevolent" agents who support human moral flourishing. The project is based on the Aristotelian understanding of benevolence as wishing the good of another person for their own sake, and malevolence as wishing vice or flaw upon another person. The proposed system allows users to dynamically interact and switch between a benevolent agent that supports virtue and a malevolent one that trains the user's "moral muscles" and nudges them toward vice through provocation and Socratic irony. Such an architecture prevents the risk of moral indoctrination and the creation of artificial "moral saints," while simultaneously provoking moral reflection. As a result, this system is intended to serve as a tool for moral enhancement, developing human critical moral reflection and self-understanding.

Speakers' bios:
Bartłomiej Skowron is a philosopher and Platonist working at the Faculty of Administration and Social Sciences at Warsaw University of Technology, specializing in the mathematical philosophy, ontology, phenomenology, and AI ethics.

Jarosław Chudziak is based at the same university's Faculty of Electronics and Information Technology, focusing on intelligent information systems, artificial intelligence, data engineering technologies, advanced data analytics, and knowledge representation methods.

Moderator's bio:
Ted Theodosopoulos is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level seventeen years ago, the last nine at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.
