Abstract. See https://www.dropbox.com/scl/fi/jewslfetaz2ev5jw06hd8/Abstract-Mehmet.pdf?rlkey=nk8r70udv79k9om7nwpzq3if8&dl=0.
The talks are all happening at University of Southampton (in person), on Highfield Campus (SO17 1BJ). For the building and the room, see the individual postings. Email the organiser ( b (dot) koeck (at) soton.ac.uk ) if you have questions.
More Pure Maths talks at Southampton: we run Pure Maths Colloquia, Topology Seminar, and Pure Postgraduate Seminar (link soon).
Abstract. See https://www.dropbox.com/scl/fi/jewslfetaz2ev5jw06hd8/Abstract-Mehmet.pdf?rlkey=nk8r70udv79k9om7nwpzq3if8&dl=0.
Abstract.
In today's data-driven era, advancements in cryptography have resulted in well-established and globally standardised algorithms for securing data at rest (using symmetric-key encryption) and data in transit (through public-key encryption and TLS). In recent years, researchers have increasingly focused on addressing the question: Can we use the data without compromising its privacy or security? The answer is yes! While some cryptographic techniques may appear impractical in certain situations, extensive research has made computing on encrypted data (COED) techniques more applicable to real-world solutions.
The primary COED techniques are multi-party computation (MPC), homomorphic encryption, and zero-knowledge proofs. MPC employs secret-sharing techniques, enabling multiple parties to evaluate a function collaboratively without gaining knowledge about each other's inputs. Its applications range from secure auctions and voting systems to fraud detection algorithms. Following an introduction to MPC, this seminar will focus on privacy-preserving machine learning (ML), specifically, using MPC to train and evaluate ML models securely. We will conclude with a brief introduction to homomorphic encryption and zero-knowledge proofs.
Abstract: We can associate to a group G = G_1 * G_2 * ... * G_n an 'outer space' on which the outer automorphism group Out(G) acts. By studying this space (or a subcomplex of it), we can apply a theorem of Brown to extract a presentation for Out(G) which is both concise and intuitive. We demonstrate this in the case n=3, which has a particularly pleasing form, and reaffirms a result of Collins and Gilbert, and suggest how this can be generalised.
Abstract. The notion of retraction in groups have popped up from a variety of topics, such as, surface groups, RAAGS, fundamental groups of cube complexes and model theory in groups.
We say that a subgroup H is a virtual retract of a group G when H is a retract of a finite index subgroup of G. If all cyclic/f.g subgroups of G are virtual retracts, we say that G has (LR)/(VRC).
I will give an overview of why properties (LR)/(VRC) may be of interest to geometric group theorist, and then expand on some questions regarding the problem itself; if G has (LR)/(VRC), what about its quotients?; if a quotient of G has (LR)/(VRC), what about G?; if a family of groups have (LR)/(VRC), what about their free product or other free constructions?
Abstract: The area of set optimization is under rapid development. The set relation approach ''opens a new and wide field of research'' and set relations ''turn out to be very promising in set optimization.'' In this talk, I will discuss the answer of some of the following questions:
1. What is set-valued optimization and motivation to consider set-valued optimization problems?
2. Which kind of methodology should be used for a particular decision?
3. What should be understood by a solution of an optimization problem?
4. How can a corresponding set-valued optimization theory be developed?
Abstract. I will explain what is known about several different classifications of 4-manifolds (up to diffeomorphism, homeomorphism, homotopy equivalence...) and the relations between the different classifications.