Fridays@4

Speaker: Ximena Laura Fernandez
Title: Let it Be(tti): Topological Fingerprints for Audio Identification

Abstract: Ever wondered how music recognition apps like Shazam work or why they sometimes fail? Can Algebraic Topology improve current audio identification algorithms? In this talk, I will discuss recent collaborative work with Spotify, where we extract low-dimensional homological features from audio signals for efficient song identification despite continuous obfuscations. Our approach significantly improves accuracy and reliability in matching audio content under topological distortions, including pitch and tempo shifts, compared to Shazam.

Talk based on the work: https://arxiv.org/pdf/2309.03516.pdf
 

Speaker: Brett Kolesnik
Title: Coxeter Tournaments

Abstract: We will present ongoing joint work with three Oxford PhD students: Matthew Buckland (Stats), Rivka Mitchell (Math/Stats) and Tomasz Przybyłowski (Math). We met last year as part of the course SC9 Probability on Graphs and Lattices. Connections with geometry (the permutahedron and generalizations), combinatorics (tournaments and signed graphs), statistics (paired comparisons and sampling) and probability (coupling and rapid mixing) will be discussed.

What opportunities are available outside of academia? What skills beyond strong academic background are companies looking for to be successful in transitioning to industry? Come along and hear from video technology company V-Nova and Dr Anne Wolfes from the Careers Service to get some invaluable advice on careers outside academia.

Speaker: Lasse Grimmelt (North Wing)
Title: Modular forms and the twin prime conjecture

Abstract: Modular forms are one of the most fruitful areas in modern number theory. They play a central part in Wiles proof of Fermat's last theorem and in Langland's far reaching vision. Curiously, some of our best approximations to the twin-prime conjecture are also powered by them. In the existing literature this connection is highly technical and difficult to approach. In work in progress on this types of questions, my coauthor and I found a different perspective based on a quite simple idea. In this way we get an easy explanation and good intuition why such a connection should exists. I will explain this in this talk.

Speaker: Yang Liu (South Wing)
Title: Obtaining Pseudo-inverse Solutions With MINRES

Abstract: The celebrated minimum residual method (MINRES) has seen great success and wide-spread use in solving linear least-squared problems involving Hermitian matrices, with further extensions to complex symmetric settings. Unless the system is consistent whereby the right-hand side vector lies in the range of the matrix, MINRES is not guaranteed to obtain the pseudo-inverse solution. We propose a novel and remarkably simple lifting strategy that seamlessly integrates with the final MINRES iteration, enabling us to obtain the minimum norm solution with negligible additional computational costs. We also study our lifting strategy in a diverse range of settings encompassing Hermitian and complex symmetric systems as well as those with semi-definite preconditioners.

Job applications involve a lot of work and can be overwhelming. Join us for a workshop and Q+A session focused on breaking down academic applications: we’ll talk about approaching reference letter writers, writing research statements, and discussing what makes a great CV and covering letter.

How do you make the most of graduate supervisions?  Whether you are a first year graduate wanting to learn about how to manage meetings with your supervisor, or a later year DPhil student, postdoc or faculty member willing to share their experiences and give advice, please come along to this informal discussion led by DPhil students for the first Fridays@4 session of the term.  You can also continue the conversation and learn more about graduate student life at Oxford at Happy Hour afterwards.

Title: Elliptic curves and modularity

Abstract: The goal of this talk is to give you a glimpse of the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. I will focus on a celebrated instance of the Langlands correspondence, namely the modularity of elliptic curves. In the first part of the talk, I will give an explicit example, discuss the different meanings of modularity for rational elliptic curves, and mention applications. In the second part of the talk, I will discuss what is known about the modularity of elliptic curves over more general number fields.

In recent years, methods and concepts of algebraic geometry, particularly those of real and computational algebraic geometry, have been used in many applied domains. In this talk, aimed at a broad audience, I will review applications to molecular biology. The goal is to analyze standard models in systems biology to predict dynamic behavior in regions of parameter space without the need for simulations. I will also mention some challenges in the field of real algebraic geometry that arise from these applications.