Integration BeeMarch 27, 20255:30 PM–7:00 PM |
| Time | Speaker | Title | Abstract | |
|---|---|---|---|---|
| 1 | Jeff Luo | Spherical Geometry | A short, low-tech introduction to spherical geometry and some nice computational results. | |
| 2 | Elizabeth Cai | Hirzebruch Surfaces in Toric Varieties | Hirzebruch surfaces, fundamental examples of toric varieties, play a crucial role in mirror symmetry due to their rich combinatorial structure and well-understood geometry. In this seminar, we explore their toric description, emphasizing the polytope structure and the associated fan construction. We then examine how mirror symmetry manifests in this setting, particularly through the lens of toric degenerations, Landau-Ginzburg models, and the role of SYZ duality. By leveraging explicit calculations in toric geometry, we highlight key features of mirror pairs and discuss how these ideas generalize to broader classes of varieties. This talk aims to provide an accessible introduction to the interplay between Hirzebruch surfaces, toric methods, and mirror symmetry. | |
| 3 | Shalev Manor | WTF Is a PINN? A Brief Introduction to Physics Informed Neural Networks | Standard fully connected neural networks utilize training sets of input-output pairs to optimize their internal parameters towards the approximation of a function. This approach has been shown to have a wide range of applications in everything from image recognition to fraud detection. However, reliable performance with these models typically requires extremely large training datasets, which are often prohibitively expensive or impractical to obtain. For certain types of problems, we may already have existing knowledge on how we expect solutions to behave (i.e. problems involving physics). Physics Informed Neural Networks (PINNs) successfully incorporate our existing understanding of physical laws into their training process. They require far fewer training samples to perform adequately while enforcing compliance with physical laws. In this talk, I will give a brief introduction to the Multi-Layer Perceptron (MLP) architecture and introduce the ideas utilised in Physics Informed Neural Networks along with some related methods. | |
| Keynote Speaker | Prof. Jochen Könemann | Fast & Simple Algorithms for Multicommodity Flow | We will present a brief overview over simple, and fast first-order techniques to solve structured linear programs. These techniques have seen countless applications, and remain popular in many applications. |
|
| 5 | Kathryn Froese | Lie Algebras, Nuclear Chemistry, and Shelf-Stable Chocolate Milk | In nuclear chemistry, one is interested in resonance phenomena of the molecules involved. It turns out they have a deep connection to Lie theory and Cartan subalgebras of the Lie algebra of the symmetry group. This all has shocking consequences on the chemistry of your food, including the beloved Milkis. | |
| 6 | Alex Pawelko | Russian Man Approximates Eigenvalues With This One Weird Trick, Mathematicians Hate Him! | One of the central themes of linear algebra is the importance of eigenvalues and spectral theory for understanding the behavior of matrices. As such, many applications of linear algebra require efficient and reliable methods to compute and approximate eigenvalues. In this talk, we will discuss one such method, the Gershgorin Circle Theorem, and investigate some of its important theoretical and computational applications within linear algebra. | |
| 7 | Lia Varghese | Leveraging Simple Molecular Representations to Pre-screen Drug Molecules | Drug discovery is a complex and computationally intensive process, especially when screening large molecular databases for potential drug candidates. This research focuses on improving the efficiency of molecular screening by leveraging simplified molecular representations. Specifically, we explore the use of MACCS fingerprints and machine learning models to prescreen molecules before running them through ConPLex, a state-of-the-art drug-protein interaction model. Molecules are selected based on location a high dimensional vector space and resulting cosine-similarity clusters. | |
| 8 | Lexy Lawryshyn | Travelling Waves of the Diffusive Streeter-Phelps Equations with Braun-Berthouex BOD Decay | Travelling Waves of the Diffusive Streeter-Phelps Equations with Braun-Berthouex BOD Decay | |
| 9 | Robert De Castris | Fractal Image Compression | Fractal image compression was devised in the 80s as an alternative to other image compression methods, such as the discrete cosine transform. Though the method has faded somewhat from relevance in recent years, it remains a mathematically beautiful application of analysis and fractal theory. One of the key advantages of the method is the relative simplicity of its implementation. We present a rudimentary yet effective implementation of a fractal image encoding and decoding scheme which is capable of producing greyscale and RGB coloured images. Potential issues and areas for improvement of the implementation are discussed, with a focus on the issue of missing pixels. | |
| 10 | Vinay Joshy | Generative Score-Based Models: Reverse Engineering Noise | Score-based generative models estimate the gradient of the log probability density to enable efficient sampling. This presentation explores their theoretical foundations, implementation, and applications, focusing on novel noise perturbation methods and applications | |
| 11 | Patrik Buhring | Desmos Shenanigans 2: Electric Boogaloo | Have you ever wondered just how far you can push Desmos? This talk will aim to explore some of the more arcane things you can do with Desmos, and hopefully be equally as entertaining as it is insane. | |
| 12 | Björgvin Aa | Categorical Limits and their Topological Cousins | "Category theory is often viewed (sometimes rightfully so) as silly abstract nonsense. It is, however, ubiquitous and finds applications in every modern algebraic field (algebraic geometry, algebraic topology, homological algebra, etc.) Some of you may already be familiar with universal properties and how they aid in constructing various algebraic objects. We will cover basic definitions, provide some intuition and constructions, and ultimately show the definition of the limit of a diagram. Why does this have the same name as a (topological) limit (as seen in Math 137/8)? It’s mostly a coincidence, though there are some interesting connections. In particular, we will present a categorical construction of the (topological) limit of a certain filter. (subject to change/might not include everything depending on timing constraints)." | |
| 13 | Alex Pawelko | Differential Geometers Suck At Naming Things | In this talk, I will explain enough differential geometry for my jokes that make fun of differential geometers to be funny. | |
| 14 | Mars Xiang | Simple and Strong Bounds for Maximum Matching | Maximum matching is one of the most straightforward algorithmic problems, bringing with it a variety of solutions in the classical model of computation. Yet in the streaming model, where data too large to store in memory is revealed bit by bit, whether the "trivial" algorithm is optimal is still an open question! In this talk, we prove that no streaming algorithm can reliably output a matching more than s times the size of the maximum matching (where s ∈ [~0.548, 2/3] is a number that depends on the seriousness of this talk), nearly matching the 1/2-bound the "trivial" algorithm guarantees. | |
| 15 | River Stanley | Is Karl Marx Bisexual (Part I): Deconstructing Text-Based Document Retrieval Evaluation Methods | An AMATH/CS talk about the mathematical approaches used by text-based retrieval engines (e.g. google search), with particular focus on the BM25 method and probabilistic relevance modelling. Outline: * wtf is a document: Basic overview of why we need search engines. Introduces notions of precision/recall and optimizing their tradeoffs. * wtf is a search: How search engines produce results. Introduces the basic idea of the search pipeline. * wtf is a rank: How search engines weight documents relative to others; presents a mini overview of some options. * wtf is a BM25: Introducing the BM25 equation, and deconstructing why it works. Discusses topics of term, document frequencies, impact of document length, and how BM25 combines them. * (if sufficient time) wtf is a covariance: Discusses relevance modelling approaches to improve document recall by leaning on probability models of word likelihood. |
|
| 16 | Sara Nayar | Teaching You Fractions | We all know what fractions are. More specifically, we know what the rational numbers are—ratios of integers. I claim you've barely scratched the surface of what fractions can be! We'll be talking about fraction fields and localization, commutative and noncommutative. | |
| 17 | Aliyah Knetsch | R Sucks | The programming language R really sucks. In this talk, we'll dive deep into its cursed features. | |
| 18 | David Teresi | Every Map of Hamilton is Wrong | We attempt to fix the map of Hamilton, Ontario using advanced geographic projection techniques. | |
| 19 | Grace Feng | MathSoc Council Meeting Simulator: Sponsored by MathSoc | MathSoc brings all the comforts of a regular Council meeting to your front door! | |
| 20 | TBA | |||
| 21 | Alex Stan | I Really Fucking Love Stalker 2 | I will talk about stalker 2 and ukrainian post-apocalyptic single player games for 30 mins. | |
| 22 | Yi Fan Song | My Factorio Addiction | I show my factorio factory. | |
| 23 | Liam Gardner | The Empty Talk | [Empty] | |
| 24 | Charles Qiu | Analytic Chemistry | I will create a tier list of all 118 chemical elements (or as many as time allows) based on "vibes", with audience input on tiering. | |
| 25 | Sara Nayar | Hollow Knight Speedrunning and the Topology Rule | In order to display the many practical applications of homotopy theory, we'll be discussing limitations on Hollow Knight's Any% No Major Glitches category. | |
| 26 | Remington Zhi | Math Wikipedia Tea | Wikipedia articles come with a talk page where editors discuss its contents and edits. This is a site of lively debate. We're gonna take a stroll through some of my favourite arguments that I found in the 1-2 hours I prepared for this talk. | |
| 27 | Isabela Souza | Brazilian Memes 101 | A brief introduction to Brazilian meme culture. | |
| 28 | Yi Fan Song | Close Your Eyes and Trust me | If I tell you that I know a secret number, would you believe me? What would I need to tell you in order for you to believe me, I don't want to tell you my number. I also don't want to tell you anything that will let you compute my number. So can you trust me? Well, the answer is maybe, if you ask the right questions, and then if you ask me again, you'll be convinced a little bit more, and keep asking me until you are fully convinced. |
|
| 29 | Charles Qiu | Summer Break Activities | I am going to read through every entry of the Canadian Criminal Code with incredibly weak justifications of why it would be a fun thing to do | |
| 30 | Elyn Huang | The Math Behind Making a Pie | As we all know making a pie is very hard because it can easily fall apart when putting it into a mold out of the fridge. So, we do need to do some math and some calculations before putting liquid, flour and oil, and mix them together. | |
| 31 | Connor Baetz | The Ancient World and Parabolas | Rederiving as much information as possible about parabolas with as little algebra as possible. Hopefully ending with the oldest use of a geometric series. | |
| 32 | River Stanley | Is Karl Marx Bisexual (Part II): Probabilistic Models in Search | An AMATH/CS talk addressing the issue of methods used to correlate seemingly-unrelated words in text-based retrieval. Discusses: * Query likelihood retrieval: a search retrieval ranking method leveraging the probability of each term to be found in the collection * Relevance feedback: methods by which result sets can be used to train the retrieval engine to improve later results * RM3 Relevance modelling: combining pseudo-relevance feedback with query likelihood retrieval to make search engines smarter faster. also dumber faster. |
|
| 33 | Abhipsha Sahu | A Physicist's Guide to Disrespecting Math | Physics is best known for two things: advancing our knowledge of the universe, and having absolutely no respect for mathematicians in the process. While mathematicians might attempt to introduce rigor and formality to our framework of scientific exploration, this talk goes through the myriad of ways physicists might take that thirst for rigor—and burn it to the ground. | |
| 34 | Anthony Rafael Tan | An Indonesian's First Experience of Canada | Presenting first impressions and experiences of Canada, classing that I'm currently taking, Canada/Waterloo culture shocks and the Waterloo experience as a "research student". More of a fun talk / discussion to get to know people and connect with the MathSoc Community. |
|
| 35 | Evan Girardin | Leaving MC | We will follow in Evan's footsteps and leave MC (forever???) | |
| 36 | Remington Zhi | Single-Transferable Vote and How WUSA Does It Wrong | The Single-Transferrable Vote (STV) is an electoral system in which voters cast a ballot ranking their prefered candidates, and multiple seats are elected. It is often seen as the most manipulation-proof voting system that is reasonably simple to implement—in fact, it was the first to be proven to be NP-complete to manipulate. In this talk, we will first review a collation of literature on the difficulty of manipulation STV (with no proofs because I don't understand CO. Why did I choose this topic). Then, we will examine a close-to-home example of the WUSA 2024 and 2025 General Elections. We will use the published vote counts to reverse-engineer WUSA’s redistribution algorithm, and loot at how additional stipulations on seat allocation can defeat the manipulation-resistance of STV. | |
| 37 | Liam Benoit | Chebyshev Sets in Hilbert Spaces | In optimization and approximation theory, we often explore questions of the form "Given some point x and a set C, what is the closest point in C to x?" Sets where such a closest point exists and is unique for all x are called Chebyshev sets. I will "prove" (up to blackboxing some technical analysis or geometry results) that, in Euclidean spaces, Chebyshev sets are closed and convex. If time permits, I will talk about Chebyshev sets in Hilbert spaces, where it is still unknown whether or not they must be convex. | |
| 38 | Sophie Twardus | The Math I Actually Use at StatCan | You have graduated, you get a job in the real world. What math from your degree was actually relevant? What kind of annoying problems come up. This talk will consider the case study of Census Non-Response Rate, Foreign Investors in Canadian Housing, and Census of Labour Occupation Auto-coding | |
| 39 | Awab Qureshi | 5D Programming with Multi-versal Time Travel (aka. Losing our minds with ""practical"" multithreading) | What's better than one processor? How does our mental model change when instead of one execution of our program, we have many running concurrently? Why two processors of course! How do we practically harness this curse power? Do computers even run your code??? And how do stRACE CONDITIONop from minlose ds? Surely this will not go wrong.. | |
| 40 | Christian Choi | PMATH 351 in 30 Minutes | Many people walk away from PMATH 351 without gaining a deep understanding of real analysis, which is unfortunate because the topics covered in it are both useful and very cool in their own right. In this talk I will share my enthusiasm for the course by developing intuitions for the major concepts and theorems from the ground up. | |
| 41 | Noah Nazareth | Proof of Compactness Using Ultraproducts | Compactness is a strong result in logic that is often proved using notions of proofs. But why would you want to develop proof theory, when you can just do more extreme model theory (which I'll call ultra model theory) and get the result in-house. | |
| 42 | Bryan Chen | Where do your numbers come from? | We will discuss (pseudo)random number generators, why we need them and some notable examples of these and how they work, as well as what happens if you mess up the implementation and what happens when you are a little… TOO random… | |
| 43 | Sasha Novikov | Applications of Graph Theory to Register Allocation | When we build higher-level languages from assembly langs, an abstraction we really desire to have is variables. Register allocation is one of the ways variables can be implemented. However, solving this problem is NP-complete. We will therefore look at some other ways to solve this problem. | |
| 44 | Edmond | Cheese Paradox and Multivariable Calculus | Cheese has holes More cheese = more holes more holes = less cheese therefore more cheese = less cheese We explain this paradox formally with multivariable calculus and use this to explain a few well known counterintuitive equations. |
|
| 45 | Kavin Satheeskumar | The Hadwiger-Nelson Problem | My favourite open problem :D | |
| 46 | Easty Guo | the Choquet Boundary + Motivation | In one of my previous SASMS talks, I introduced and proved Korovkin's theorem. Here, we will see some strategies for generalizing this theorem which will lead to the definition of the Choquet boundary. Pre-reqs: math247/pmath333 at least, preferably pmath351 or higher. |
|
| 47 | Alina Hu | Girl Math | Girl Math is a powerful tool that explains the logic behind everyday financial decisions and lifestyle choices through a lens of mathematical reasoning. Beyond finances, Girl Math also tackles the infamous “I have nothing to wear” dilemma by modelling outfit selection as a combinatorial optimization problem—accounting for weather, event appropriateness, and the legally mandated no-repeat window. If it takes you only 30 minutes to pick an outfit, you’re not indecisive—you might just be a genius in disguise. | |
| 48 | Christian | Using Math to Jump for the Beef | High-level, technical Minecraft parkour surprisingly has a non-negligible amount of math involved. This is due to "frames" being relatively long compared to most other platformers. Because of this, we can both rigorously prove our intuitions and put theory into practice with consistent "frame-perfect" inputs. In this talk I will prove two important theorems in technical parkour and show practical examples for each. |
Title: Mason's conjectures for graphs
Abstract: Much of the work of recent Fields medalist June Huh is related to proving log-concavity statements related to a certain generalization of graphs called matroids. One such example was the resolution of the Mason's conjectures with Petter Brändén (also proven independently by Anari-Liu-Oveis Gharan-Vinzant), which we now describe for graphs. Given a graph G, let c(k) denote the number of subforests of G with k edges. Then c(0), c(1), …, c(n) forms a log-concave sequence, which means that c(k)^2 >= c(k-1) * c(k+1) for all k. The proof uses the exciting new machinery of Lorentzian polynomials which has seen many applications in combinatorics and computer science. In this talk, I will go through the proof of this result for graphs, which will utilize an interesting mix of basic calculus, graph theory, and linear algebra.
Title: Language Models for Many-Body Physics
Abstract: Natural language processing (NLP) tasks can be extremely complex, yet recent “language models” have achieved remarkable success. Well-known examples include ChatGPT, Gemini, DeepSeek, which perform at near-human levels on a wide range of tasks such as speech recognition, machine translation, and text generation. Surprisingly, these models are also useful for problems outside of NLP.
In this talk, I will show how we can adapt language models—particularly recurrent neural networks (RNNs)—to study quantum many-body systems. By carefully modifying and training RNNs for physics problems, we obtain state-of-the-art results that rival traditional methods originally designed by physicists. This highlights the exciting possibility of bringing insights from modern AI research to many-body physics.