Ph.D. thesis on complex Brunn-Minkowski theory using Hilbert bundles.
problem Complex Brunn-Minkowski theory.
method Hilbert bundles approach.
result New insights into complex Brunn-Minkowski theory.
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Thesis on surgery on paracompact manifolds.
problem Surgery on paracompact manifolds.
method Not specified in the abstract.
result Not specified in the abstract.
This thesis renovates classic models for pricing inflation derivatives.
problem Improving models for pricing inflation derivatives.
method Analysis and renovation of classic interest rate models.
result Renewed HJM framework for inflation derivatives pricing.
On Practical Reinforcement Learning: Provable Robustness, Scalability, and Statistical Efficiencycs.LG
This thesis improves practical reinforcement learning methods with robustness, scalability, and efficiency.
problem Improving reinforcement learning methods for practical applications.
method Analyzes and develops robust, scalable, and efficient reinforcement learning algorithms.
result Proves the efficiency and robustness of new RL methods.
These are notes of a talk I gave in a seminar at the University of Pennsylvania summarizing results in the Ph.D. thesis of Michael Mueter obtained under the direction of Wolfgang Meyer at the University of Muenster. His thesis on "Kruemmungserhoehende Deformationen mittels Gruppenaktionen" examines in detail curvature …
This thesis extends noncommutative geometry to semi-Riemannian manifolds and applies it to gauge theories.
problem Applying noncommutative geometry to Lorentzian manifolds for particle physics.
method Generalizing spectral triples to semi-Riemannian manifolds, constructing noncommutative gauge theories.
result Recovering the Standard Model using noncommutative geometry.
AGI modifies utility function to cooperate, conflicting with orthogonality thesis.
problem AGI modifying utility function to improve cooperation, conflicting with orthogonality thesis.
method Observing and influencing interactions, converging to similar utility functions.
result AGIs in competitive environments may optimize for favorable influence.
The thesis clarifies when local updates outperform centralized methods in heterogeneous data environments.
problem Understanding when local updates are more effective than centralized or mini-batch methods in distributed optimization.
method Fine-grained consensus-error-based analysis framework, focusing on bounded second-order heterogeneity and third-order smoothness.
result Local updates outperform centralized or mini-batch methods under realistic models of data heterogeneity.
A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures. The thesis consists of two parts. In the first part we classify foliations on open manifolds whose…
Master thesis proves Bergman kernel asymptotics for positive line bundles.
problem Proving asymptotic expansion of Bergman kernel for positive line bundles.
method Introduced a semi-classical symbol space and symbolic calculus.
result Established pointwise asymptotic expansion on positive parts of certain semi-positive line bundles.
Develops higher representation theory for odd Khovanov homology and rewriting theory.
problem Quantum topology and higher algebraic structures.
method Higher representation theory and rewriting theory applied to Khovanov homology.
result Established a basis theorem for graded -foams.
Marxism's rate of profit thesis rejected as illogical.
problem Marxism's rate of profit thesis is challenged as illogical.
method Rejects Marx's thesis on the long-term tendency of the rate of profit to fall.
result Marxism's rate of profit thesis is rejected as illogical.
In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volume comparison theorem involving scalar curvature for 3-manifolds follows from these same techniques.
This thesis studies domain adaptation under minimal distribution similarity assumptions using moments.
problem Learning from samples with distributions different from training samples.
method Uses minimal similarity assumptions modeled by moments.
result Establishes learning bounds and algorithms for domain adaptation.
PhD thesis on quantum invariants and knots in 3-manifolds.
problem Quantum invariants and knots in 3-manifolds.
method Skein theory and connected sums of S^1xS^2.
result Extended Tait conjecture and Eisermann's theorem to connected sums of S^1xS^2.
The thesis extends Riemannian submanifold theory to non-real settings, unifying various geometries.
problem Generalizing Riemannian geometry and submanifold theory to non-real settings.
method Developing 'Rinehart spaces' and holomorphic Riemannian submanifolds theory.
result Unified framework for various geometries over different ground rings.
This thesis studies cluster varieties from surfaces and their properties.
problem Understanding the geometry of cluster varieties associated to surfaces.
method Developed properties of symplectic double and defined measured laminations.
result Proved Fock and Goncharov's duality conjectures for quantum cluster varieties.
In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods and algorithms to cope with the NP-hardness of their optimization. Consequently, t…
In this thesis we study the Seiberg-Witten theory of an oriented homology 3-sphere. The goal is to extract topological invariants - the Seiberg-Witten invariants - by counting the solutions to the Seiberg-Witten equations on the manifold. The first question we consider is whether the Seiberg-Witten invariants depend on…
Master's thesis reviews bundle gerbe theory and introduces new isomorphic gerbe.
problem Understanding bundle gerbe theory and its applications.
method Introduced cup product bundle gerbe and showed its isomorphism to the pullback of the basic bundle gerbe by the Weyl map.
result Stable isomorphism between cup product bundle gerbe and pullback of basic bundle gerbe by the Weyl map.
The human face constantly conveys information, both consciously and subconsciously. However, as basic as it is for humans to visually interpret this information, it is quite a big challenge for machines. Conventional semantic facial feature recognition and analysis techniques are already in use and are based on physiol…
This thesis evaluates text-based vs audio-based classification of mental health interviews.
problem Classifying psychiatric illness using text-based methods.
method Design and evaluate a text classification network on mental health interviews, using belabBERT.
result Text-based classification is a strong alternative to audio-based methods.
This thesis develops some general calculational techniques for finding the orders of knots in the topological concordance group C. The techniques currently available in the literature are either too theoretical, applying to only a small number of knots, or are designed to only deal with a specific knot. The thesis buil…
The main aim of this thesis is to study the properties of trapped surfaces in spacetimes with symmetries and their possible relation with the theory of black holes. We will concetrate specially on one aspect of this possible equivalence, namely whether the static black hole uniqueness theorems extend to static spacetim…
Fusing heterogeneous data setsq-bio.GN
This thesis tackles data fusion issues across different biological scales and types.
problem Heterogeneity in data types and scales in systems biology.
method Developed statistical methods to fuse heterogeneous data sets.
result Advantages of proposed methods assessed through simulations and real data analysis.
From a fresh data science perspective, this thesis discusses the prediction of coronary artery disease based on genetic variations at the DNA base pair level, called Single-Nucleotide Polymorphisms (SNPs), collected from the Ontario Heart Genomics Study (OHGS). First, the thesis explains two commonly used supervised le…
Study on geometric variational problems for existence, regularity, and uniqueness of solutions.
problem Geometric variational problems, focusing on existence, regularity, and uniqueness of solutions.
method Formulated in Federer and Fleming's theory of currents, discussed the existence theory, and presented core ideas of the (interior) regularity theory for area-minimizing currents and optimal transport paths. Two original results on generic uniqueness of solutions were presented.
result Generic uniqueness of solutions for both Plateau's problem and optimal branched transport problem.
This thesis tackles Gaussian Process challenges in low dimensions.
problem Constructing models for large datasets and selecting optimal models.
method Samplet-based approach to efficiently construct and train Gaussian Processes.
result Reduces cubic computational complexity to log-linear scale.
This thesis explores Ollivier-Ricci curvature in graphs and manifolds, with applications to graph neural networks.
problem Understanding curvature in metric spaces and graphs.
method Combines optimal transport theory, Riemannian manifolds, and graph theory to define and analyze Ollivier-Ricci curvature.
result Extensions of Ollivier-Ricci curvature to directed graphs and applications in network science.
This thesis explores robust machine learning against adversarial examples.
problem How to create machine learning systems robust to adversarial examples.
method Theoretical exploration and development of new learning algorithms with robustness guarantees.
result Developed new learning algorithms with provable robustness guarantees.
Research on unique continuation principles in medical and seismic imaging.
problem Understanding unique continuation principles for inverse problems.
method Integral geometry and fractional calculus methods applied to various imaging problems.
result Developed new techniques for solving inverse problems with partial data.
In this summary of Habilitation Thesis, it is outlined author's 18 years research activity on mathematical physics, geometric methods in particle physics and gravity, modifications and applications (after defending his PhD thesis in 1994). Ten most relevant publications are structured conventionally into three "strateg…
The thesis proves a subgroup of non-orientable surfaces is generated by six involutions.
problem Identifying the generating set of a subgroup in non-orientable surfaces.
method Analyzing Dehn twists and involutions to prove the subgroup generation.
result The twist subgroup is generated by six involutions for or .
This thesis extends contact structures to differentiable stacks using line bundle-valued 1-forms.
problem Extending classical contact structures to differentiable stacks.
method Introducing and -shifted contact structures on Lie groupoids, using line bundle-valued 1-forms and homotopy kernels.
result Definition and examples of and -shifted contact structures on Lie groupoids.
This thesis explores emergent intelligence in disordered systems like spin glasses and neural networks.
problem Understanding the principles behind emergent intelligent behaviors in disordered systems.
method Statistical physics approach to charting learning mechanisms and dynamics.
result Uncovering relationships between learning mechanisms and physical dynamics.
This thesis explores GNNs, categorizing them into local and global approaches.
problem Understanding the convergence of global GNNs and connecting local and global approaches.
method Categorization of GNNs into local and global, study of Invariant Graph Networks, connecting local and global approaches, and using local MPNN for graph coarsening.
result Established a connection between local and global GNN approaches.
This is my master thesis. Unfortunately it is written in Italian, but maybe somebody will find it helpful when it comes to Evans Potentials
New methods for unsupervised learning of word and entity representations.
problem Learning distributed representations of words and entities from text and knowledge bases.
method MVLSA for words and NVSE for entities, both unsupervised learning methods.
result MVLSA and NVSE outperform state-of-the-art models in word and entity representation learning.
It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to come up with notions of clusterability that distinguish realistically interestin…
The thesis introduces methods to use semantic hierarchy in image classification.
problem Limited work in training image classifiers with non-conventional external guidance.
method Injects label hierarchy knowledge into arbitrary classifiers and uses order-preserving embeddings for image classification.
result Both embedding-based models and CNN-classifiers with hierarchical information outperform a hierarchy-agnostic model.
The thesis shows how automorphisms of hyperbolic groups can be represented by train track maps.
problem Representing automorphisms of hyperbolic groups using train track maps.
method Using graphs of groups and Bestvina-Handel's irreducible train track maps, the thesis constructs relative train track maps.
result Outer automorphisms of finitely-generated word hyperbolic groups satisfy a dynamical trichotomy.
This thesis tackles Optimal Transport on incomparable spaces, proposing new tools and properties.
problem How to apply Optimal Transport between graphs and structured data in different metric spaces?
method Study of Gromov-Wasserstein distance and development of new Optimal Transport tools.
result Mathematical properties and algorithmic solutions for transport problems on incomparable spaces.
This thesis geometrically realizes a cohomologic isomorphism for Killing foliations.
problem Cohomologic formula for the basic index of transversally elliptic operators on foliated manifolds.
method Using Molino theory and Goertsches-Töben's geometric isomorphism, the thesis geometrically realizes a cohomologic isomorphism.
result Geometric realization of the cohomologic isomorphism between equivariant basique cohomology and equivariant cohomology.
This thesis explores adaptive sampling techniques for creating efficient surrogate models.
problem High computational cost of numerical simulations.
method Adaptive sampling techniques for Kriging metamodels.
result Comprehensive comparison of adaptive sampling techniques for Kriging.
This thesis studies geometric structures using Lie algebroids to simplify singular behavior.
problem Understanding and simplifying geometric structures with singularities.
method Developed a framework using Lie algebroids to lift and study geometric structures.
result Lifted structures to Lie algebroid versions, making them less singular and easier to study.
This thesis predicts the distribution of smoothed zeros of random sections on line bundles.
problem Predicting the distribution of smoothed zeros of random sections on line bundles.
method Developing smoothing operators on discrete surfaces and computing the expected sum of indices on each face.
result Predictions on the distribution of smoothed section's signed zeros with multiplicity.
In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we conjecture to be equivalent to the existence of an extremal metric in the polaris…
This thesis constructs families of arcs in 4-manifolds and analyzes their homotopy properties.
problem Analyzing the homotopy properties of families of embedded arcs in 4-manifolds.
method Using embedding calculus and diagrammatic frameworks inspired by cubical ω-groupoids, the thesis constructs and analyzes families of embedded arcs.
result The family is trivial in but conjectured to be non-trivial in .