The meeting spans two days. Day 1 will feature an introduction to machine learning and algebraic geometry by Sara Veneziale (Imperial), and Day 2 will feature talks by Matthew England (Coventry), Yang-Hui He (LIMS), and Rob Silversmith (Warwick).
To attend, please register here.
All activities will take place in B3.03 in the Zeeman building (Maths). An interactive campus map is here. Breaks will be in the common room, which is on the 1st floor (enter the department by the doors to the left as you enter the building, and go up one flight of stairs). From the common room, go up two more flights of stairs for B3.03, which is then on the right.
13:00 - 17:00 Sara Veneziale (Imperial): Machine Learning and Algebraic Geometry (practical tutorial)
09:30 - 10:15 Yue Ren: OSCAR tutorial
10:45 - 11:30 Diane Maclagan: M2 tutorial
13:00 - 14:00 Rob Silversmith. Cross-ratio degrees
14:30 - 15:30 Matthew England. Real quantifier elimination technology and optimisations via Machine Learning
16:00 - 17:00 Yang-Hui He. The AI Mathematician: From Physics, to Geometry, to Number Theory
Rob Silversmith Cross-ratio degrees
Abstract: The cross-ratio degree problem is a simple class of counting problems in combinatorial
algebraic geometry. I’ll discuss the problem and some methods for computing the answers, as well as
some special cases that an appear in an array of contexts. I'll present an upper bound on cross-ratio
degrees in terms of counting perfect matchings on bipartite graphs — whose proof involves
Gromov-Witten theory.
Matthew England Real quantifier elimination technology and optimisations via Machine Learning
Quantifier Elimination (QE) may be considered as a form of simplification in mathematical
logic: given a quantified logical statement QE will produce a statement which is equivalent
as does not involve any logical quantifiers (there exists / for all). Real QE refers to the
case where the logical atoms are constraints on polynomials over the real numbers: in this
case the work of Tarski shows that QE is always possible with algorithms relying on results
from algebraic geometry and related areas of mathematics.
The best known method for Real QE was Cylindrical Algebraic Decomposition (CAD) proposed by
Collins in the 1970s. However, CAD is known to have doubly exponential complexity, in effect
producing a wall beyond which its application is infeasible. In this talk we will introduce
QE and CAD, and describe recent algorithmic advances the author has been involved in which
"push back" that doubly exponential wall. In particular, we will focus on the optimisation
of algorithms through the use of machine learning to tune algorithm decisions while
maintaining exact results; and some recent work with explainable AI to inform computer
algebra developers to allow for better software without explicit reliance in code on AI.
Yang-Hui He. The AI Mathematician: From Physics, to Geometry, to Number Theory
We present a number of recent experiments on how various standard machine-learning algorithms
can help with pattern detection across disciplines ranging from algebraic geometry, to
representation theory, to combinatorics, and to number theory.
In particular, we focus on recent AI-assisted discovery of the Murmuration Phenomenon in
Arithmetic.