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Eric Moulines mini-series of lectures

Eric Moulines will be visiting the Heilbronn Institute of Mathematical Research as a Data Science Visitor from 27th January- 31st January. During his stay Eric will be delivering a series of lectures on Convex optimization for machine learning.

Tuesday 28th January 11:00- 12:00 G.09, The Fry Building
Thursday 30th January 13:00- 14:00, G.10, The Fry Building
Friday 31st January 10:00- 11:00, G.09, The Fry Building

Title: Convex optimization for machine learning

Abstract: The purpose of this course is to give an introduction to convex optimization and its applications in statistical learning.

In the first part of the course, I will recall the importance of convex optimisation in statistical learning. I will briefly introduce some useful results of convex analysis. I will then analyse gradient descent algorithms for strongly convex and then convex smooth functions. I will take this opportunity to establish some results on complexity lower bounds for such problems. I will show that the gradient descent algorithm is suboptimal and does not reach the optimal possible speed of convergence. I will the present a strategy to accelerate gradient descent algorithms in order to obtain optimal speeds.

In the second part of the course, I will focus on non smooth optimisation problems. I we will introduce the proximal operator of which I will establish some essential properties. I will then study the proximal gradient algorithms and their accelerated versions.

In a third part, I will look at stochastic versions of these algorithms.

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Heilbronn Colloquium – Leader

26th February 2020

University of Bristol

We are delighted to welcome Imre Leader to the University of Bristol to deliver a Heilbronn Colloquium.

Title: Partition Regular Equations

Abstract:  A finite or infinite matrix M is called ‘partition regular’ if whenever
the natural numbers are finitely coloured there exists a monochromatic
vector x with Mx=0. Many of the classical results of Ramsey theory, such
as van der Waerden’s theorem or Schur’s theorem, may be naturally rephrased
as assertions that certain matrices are partition regular.

While the structure of finite partition regular matrices is well understood,
little is known in the infinite case. In this talk we will review some known
results and then proceed to some recent developments.

The talk will not assume any previous knowledge of the area.

The colloquium will take place in Lecture theatre 2.41, Fry Building at 16:00-17:00 followed by a wine reception in the Fry Common room.

If you would like to attend the talk, please register by filling in this short registration form.

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Colloquium – Proffessor Delaram Kahrobaei, University of York

Title: Interactions between Group Theory, Cyber Security, Artificial Intelligence and Quantum Computation

Abstract:

In this talk, I explore how group theory plays a crucial role in data science and artificial intelligence as well as cyber security and quantum computation; at the same time, computer science and machine learning could help group theorists tackle some of their open problems. A second theme of the talk will be to formulate graph theoretic problems associated with computational complexity as group theoretic questions pertaining to graph groups. Lastly, we will look at the question of whether certain group-based cryptographic schemes are quantum-safe.

Brief bio:

Professor Delaram Kahrobaei holds the Chair of Cyber Security at the University of York. Prior to that, she was a Full Professor at the City University of New York. She is President and co-founder of the start-up, Infoshield Inc., and director of the York Interdisciplinary Centre for Cyber Security Research. She is an Associate Editor of Advances of Mathematics of Communication, and Chief Editor of the International Journal of Computer Mathematics: Computer Systems Theory. Her main research areas are Post-Quantum Algebraic Cryptography, Information Security, Data Science and Applied Algebra.

Further information

The talk will be held in the Fry Building, room 2.41, from 4pm – 5pm and will be followed by a drinks reception in the Maths common room.

The event is open to University of Bristol staff and students, as well as the general public.

To help us plan numbers, we ask that you please register in advance via Eventbrite.

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Heilbronn Colloquium – Maynard

16th December 2019

University of Bristol

We are very pleased to welcome James Maynard to the University of Bristol for a Heilbronn colloquium.

James is primarily interested in classical number theory, in particular the distribution of prime numbers. His research focuses on using tools from analytic number theory, particularly sieve methods, to study primes.

Title:  Approximating reals by fractions

Abstract: How well can you approximate real numbers by fractions with denominators coming from a given set? Although this old question has applications in many areas, in general this question seems impossibly hard – we don’t even know whether e+pi is rational or not!
If you allow for a tiny number of bad exceptions, then a beautiful dichotomy occurs – either almost everything can be approximated or almost nothing! I’ll talk about this problem and recent joint work with Dimitris Koukoulopoulos which classifies when these options occur, answering an old question of Duffin and Schaeffer. This relies on a fun blend of different ideas, including ergodic theory, analytic number theory and graph theory.

The colloquium will take place in Lecture theatre 2.41, Fry Building at 16:00- 17:00 on Monday 16th December followed by a wine reception in the Fry Common room. To help us plan catering, please complete the short registration form if you are planning to attend the colloquium.

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Colloquium – Peter Landrock, Cryptomathic

Title: The mathematics behind digital signatures

Public Key Cryptography as we use it, with billions of transactions being executed every day, was first developed respectively 50 years ago in the case of RSA and modular exponentiation, and 35 years ago in the case of elliptic curves. If quantum computers are developed at a sufficiently advanced level, currently used methods will no longer be considered secure due to Schor’s algorithm.

But the mathematics behind them remains fascinating and is connected to several interesting questions and conjectures in number theory, which is the main focus of the talk. Topics will include short orbits for the discrete logarithm map, and properties of primes that are congruent to 1 modulo 4.

Further information

The talk will be held in the Fry Building, room 2.41, from 4pm – 5pm and will be followed by a drinks reception in the Maths common room.

The event is open to University of Bristol staff and students, as well as the general public.

To help us plan numbers, we ask that you please register in advance via Eventbrite.

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