Professor of Mathematics
University of Alaska Fairbanks
Professor of Mathematics
University of Alaska Fairbanks
Office:
Chapman 308C
E-mail:
damaxwell@alaska.edu
Current Courses
Upcoming Courses
Presentations
Agentic AI and its Applications in 2026
UAF Math ColloquiumTime: 3:30pm-4:30pm
Date: October 16, 2026
| Lecture: | Slides | Video |
Large language models have evolved rapidly over the last couple of years: they are no longer just chatbots. Although the core architecture of LLMs remains essentially the same, a single addition, the notion of a tool call along with additional training, turns a model into an agent.
Using tool calls an LLM can initiate actions and take subsequent steps based on the outcomes of those actions. During the talk we'll review the forward pass at the heart of an LLM and then demonstrate (via interactive fiction from the 1980s!) how tool calls layered on top produce agentic behavior. The second half of the talk consists of demonstrations: coding, connecting models to data sources with the Model Context Protocol, and general knowledge work. Time will be reserved at the end for discussion.
How Large Language Models Operate
UAF Math ColloquiumTime: 1pm-2pm
Dates: November 7 and 26, 2024
| Lecture I | Slides | Video |
| Lecture II | Slides | Video |
In the last couple of years generative AI, and Large Language Models (LLMs) especially, have captured the public's attention. We've all used ChatGPT and friends by now. But how do they operate?
In this talk I aim to provide a good mental model of what is happening in the background when interacting with an LLM. I'll give an overview of how LLMs work broadly, and then dive a bit into the details of GPT-2.0, the precursor to the GPT models we use today. In particular, I'll discuss the transformer architecture, which is the foundation technology driving the current generative AI revolution.
This will be a broadly accessible talk, aimed at a general STEM audience.
An Unhelpful Introduction to Electricity and Magnetism
Fall 2020 Short Lecture SeriesTime: 1pm-2pm
Dates: Tuesday, November 10, 17 and 24 2020
Talk Link: Zoom
| Lecture I | Slides | Video |
| Lecture II | Slides | Video |
| Lecture IIIa | Slides | Video |
| Lecture IIIb | Slides | Video |
Electromagnetism is a deeply geometric physical phenomenon, an aspect that is hidden in its standard presentation. The standard presentation is efficient and effective if you want to teach people how to build radios and motors. But it turns out be be essential to understand the underlying geometry of electromagnetism when studying its relationship with general relativity, a manifestly geometric theory.
In this three-part sequence of lectures we present an unhelpful introduction to electromagnetism in the sense that it is useless for building the intuition needed to construct motors and radios and solar panels, but highlights the very simple geometric ideas and principles that give rise to electromagentism. The talks will be accessible to people with a modest mathematics background (calculus III) who have a passing interest in physics, as well as people who know far more physics than I do who would like to see a mathematician grapple with gauge theory.
The lectures:
- Part I: Really unhelpful. No physics even.
- Part II: A little physics: the emergence of E and B from geometry and symmetry.
- Part III: (That other) Maxwell's equations.