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Alexander Thomas

Publications and source records attributed to Alexander Thomas.

25 records · Page 2Linked to original sources
arXiv2022

SCL: A Secure Concurrency Layer For Paranoid Stateful Lambdas

We propose a federated Function-as-a-Service (FaaS) execution model that provides secure and stateful execution in both Cloud and Edge environments. The FaaS workers, called Paranoid Stateful Lambdas (PSLs), collaborate with one another to perform large parallel computations. We exploit cryptographically hardened and mobile bundles of data, called DataCapsules, to provide persistent state for our PSLs, whose execution is protected using hardware-secured TEEs. To make PSLs easy to program and performant, we build the familiar Key-Value Store interface on top of DataCapsules in a way that allows amortization of cryptographic operations. We demonstrate PSLs functioning in an edge environment running on a group of Intel NUCs with SGXv2. As described, our Secure Concurrency Layer (SCL), provides eventually-consistent semantics over written values using untrusted and unordered multicast. All SCL communication is encrypted, unforgeable, and private. For durability, updates are recorded in replicated DataCapsules, which are append-only cryptographically-hardened blockchain with confidentiality, integrity, and provenance guarantees. Values for inactive keys are stored in a log-structured merge-tree (LSM) in the same DataCapsule. SCL features a variety of communication optimizations, such as an efficient message passing framework that reduces the latency up to 44x from the Intel SGX SDK, and an actor-based cryptographic processing architecture that batches cryptographic operations and increases throughput by 81x.

cs.CR↗
arXiv2021

Topological quantum field theories from Hecke algebras

We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent polynomial for punctured surfaces. There is a graphical way to compute the invariant using minimal colored graphs. We give explicit formulas in terms of the Schur elements of the Hecke algebra and prove positivity properties for the invariants when the Coxeter group is of classical type, or one of the exceptional types $H_3$, $E_6$ and $E_7$.

math.QA↗
arXiv2021

Differential Operators on Surfaces and Rational WKB Method

In this paper, we give a simple and geometric, but formal, description of an open subset of the character variety of surface groups into $\mathrm{SL}_n(\mathbb{C})$. The main ingredient is a modified version of the WKB method, which we call rational WKB method. The geometric interpretation uses higher complex structures introduced by Vladimir Fock and the author. More precisely, the character variety is parametrized by the cotangent bundle of the moduli space of higher complex structures. This generalizes the well-known description of the moduli space of flat $\mathrm{SL}_2(\mathbb{C})$-connections by the cotangent bundle of Teichmüller space.

math.DG↗
arXiv2021

Generalized Punctual Hilbert Schemes and $\mathfrak{g}$-complex structures

We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple properties with Hitchin components, and which are conjecturally homeomorphic to them. For simple complex Lie algebras, this generalizes the higher complex structure. For real Lie algebras, this should give an alternative description of the Hitchin-Kostant-Rallis section.

math.DG↗
arXiv2020

Higher Complex Structures and Higher Teichmüller Theory

In this PhD thesis, we give a new geometric approach to higher Teichmüller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The construction of this structure, called higher complex structure, uses the punctual Hilbert scheme of the plane. Its moduli space admits similar properties to Hitchin's component. Given a higher complex structure, we try to canonically deform it to a flat connection. The space of such connections, called "parabolic", is obtained by imitating the Atiyah--Bott reduction. It is a space of pairs of commuting differential operators. Under some conjecture, we establish a canonical diffeomorphism between our moduli space and Hitchin's component. Finally, we generalize certain constructions, like the punctual Hilbert scheme and the higher complex structure, to the case of a simple Lie algebra.

math.DG↗
arXiv2018

Statistical characterization of microstructure evolution during compaction of granular systems composed of spheres with hardening plastic behavior

An extensive numerical campaign of particle mechanics calculations that predict microstructure formation and evolution during die compaction, up to relative densities close to one, of monodisperse plastic spheres that exhibit power-law plastic hardening behavior is presented. The study is focused on elucidating the relationship between particle plastic properties, loading conditions, and statistical features of the resulting microstructure. This communication provides fundamental insight into the achievable space of microstructures through die compaction, for given plastic stiffness and hardening exponent at the particle scale.

cond-mat.mtrl-sci↗