@misc{21971,
  abstract     = {A Rust library for analyzing dendritic structures using quadric matrices. This project provides efficient tools for representing dendritic trees, computing quadric error metrics, and visualizing eigenvalue distributions on hexagonal plots.

This library implements quadric-based geometric analysis of dendritic structures, commonly found in neuroscience applications. Key features include:

Tree data structures: Hierarchical vertex and edge representations for dendritic trees
Quadric matrices: Computation of quadric error metrics for edges and vertices
Visualisation: Hexagonal plot generation using NormPolar transformations
Interactive tools: Desktop application with plotting capabilities},
  author       = {Bleile, Yossi and Cortinovis, Emanuele},
  keywords     = {quadratics, mathematics, dendrites, geometry, topology},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Quadrix}},
  doi          = {10.15479/AT-ISTA-21971},
  year         = {2026},
}

@inproceedings{22617,
  abstract     = {Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team players randomise independently, they win with probability 1/8; if all players share a common source of randomness, they win with probability 1/2. What happens when each pair of team players shares a source of randomness? Can the team do better than win with probability 1/4? The surprising (and nontrivial) answer is yes!
We introduce Dicey Games, a formal framework motivated by the study of distributed systems with shared sources of randomness (of which the above example is a specific instance). We characterise the existence, representation and computational complexity of optimal strategies in Dicey Games, and we study the problem of allocating limited sources of randomness optimally within a team.},
  author       = {Brice, Leonard J and Henzinger, Thomas A and Thejaswini, K. S.},
  booktitle    = {41st Annual Symposium on Logic in Computer Science},
  isbn         = {9783959774345},
  issn         = {1868-8969},
  keywords     = {Concurrent games, Shared randomness, Topology, Algebraic Geometry},
  location     = {Lisbon, Portugal},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Dicey games: Shared sources of randomness in distributed systems}},
  doi          = {10.4230/LIPIcs.LICS.2026.23},
  volume       = {380},
  year         = {2026},
}

@inproceedings{22405,
  abstract     = {Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in 2D, the problem is solvable in truly subquadratic time [Chan et al., 2025], while for other objects, including unit segments and equilateral triangles in 2D or unit balls and axis-parallel unit cubes in 3D, there is no truly subquadratic time algorithm under the Orthogonal Vector (OV) hypothesis [Bringmann et al., 2022]. 
We undertake a comprehensive study of computing the diameter of geometric intersection graphs for various types of objects. We discover many new irregularities, showing that the landscape is extremely nuanced: the source of hardness is a combination of the object type, the true diameter value, and how the objects intersect with each other. Our highlighted results for the 2D case include:  
1) The diameter of non-degenerate, axis-aligned line segments can be computed in truly subquadratic time. Previous hardness result [Bringmann et al., 2022] for line segments applies only to degenerate instances. On the other hand, for the degenerate case, we show that a truly subquadratic time algorithm exists when the true diameter is constant. 
2) An almost-linear-time algorithm for unit-square graphs of constant diameter. Previous algorithms [Duraj et al., 2024; Chan et al., 2025] rely on succinct representation assuming bounded VC-dimension; for such a strategy Ω(n^{7/4}) time is an inherent barrier. 
3) An Õ(n^{4/3})-time algorithm to decide if the diameter of a unit-disk graph is at most 2. This improves upon the recent algorithm with running time Õ(n^{2-1/9}) [Chan et al., 2025]. 
4) Deciding if the diameter of intersection graphs of fat triangles or line segments is at most 2 is truly subquadratic-hard under fine-grained complexity assumptions. Previous lower bounds [Bringmann et al., 2022] only hold when deciding if diameter is at most 3.  Our findings are presented in a pair of papers. This paper focuses solely on the 2D case, while the companion paper is devoted to higher-dimensional cases.},
  author       = {Chan, Timothy M. and Chang, Hsien-Chih and Gao, Jie and Kisfaludi-Bak, Sándor and Le, Hung and Zheng, Da Wei},
  booktitle    = {53rd International Colloquium on Automata, Languages, and Programming},
  issn         = {1868-8969},
  keywords     = {String graphs, Fine-grained complexity, Theory of computation → Computational geometry},
  location     = {Egham, United Kingdom},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Charting the landscape of diameter computation on geometric intersection graphs in the plane}},
  doi          = {10.4230/LIPICS.ICALP.2026.54},
  volume       = {374},
  year         = {2026},
}

@inproceedings{22299,
  abstract     = {The depth poset of a filtered Lefschetz complex reflects the dependencies between the cancellations of different shallow birth-death pairs. Using the fast algorithms for computing the depth poset in [Edelsbrunner et al., 2026] and for updating the persistence diagram under transpositions in [Cohen-Steiner et al., 2006], we give a complete case analysis of how transpositions of cells in the filter affect the depth poset. In addition, we present statistics on the depth poset for random point data and its sensitivity to the transpositions that occur in random straight-line homotopies.},
  author       = {Edelsbrunner, Herbert and Lipiński, Michał and Mrozek, Marian and Soriano Trigueros, Manuel and Zimin, Fedor},
  booktitle    = {42nd International Symposium on Computational Geometry},
  isbn         = {9783959774185},
  issn         = {1868-8969},
  keywords     = {Algebraic topology, Lefschetz complexes, persistent homology, vines and vineyards, birth-death pairs, shallow pairs, relations, partial orders, transpositions, Theory of computation → Computational geometry},
  location     = {New Brunswick, NJ, United States},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{The depth poset under transpositions in the filter}},
  doi          = {10.4230/LIPICS.SOCG.2026.41},
  volume       = {367},
  year         = {2026},
}

@article{10011,
  abstract     = {We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow-is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle.},
  author       = {Hensel, Sebastian and Laux, Tim},
  issn         = {1945-743X},
  journal      = {Journal of Differential Geometry},
  keywords     = {Mean curvature flow, gradient flows, varifolds, weak solutions, weak-strong uniqueness, calibrated geometry, gradient-flow calibrations},
  pages        = {209--268},
  publisher    = {International Press of Boston},
  title        = {{A new varifold solution concept for mean curvature flow: Convergence of  the Allen-Cahn equation and weak-strong uniqueness}},
  doi          = {10.4310/jdg/1747065796},
  volume       = {130},
  year         = {2025},
}

@unpublished{22340,
  abstract     = {We show that Laplace isospectral deformations within a conformal class of generic Liouville metrics on the two-dimensional torus that are linear in the deformation parameter are necessarily trivial. Two of the main ingredients in our proof are a noncancellation result for the wave trace and an analysis of the second order variational formula for the energy functional associated to closed geodesics. Noncancellation allows us to detect parts of the length spectrum from the Laplace spectrum and conclude rational integrability for the deformed geodesic flow (Liouville metrics are folklorically conjectured to be the only Riemannian metrics with integrable geodesic flow on the torus). We then use the second variational formula to show how the preservation of a single rational torus is sufficient to conclude triviality of the deformation, assuming linearity. We also present some evidence that our hypothesis of linearity may indeed be necessary.},
  author       = {Henheik, Sven Joscha and Kaloshin, Vadim and Li, Yunzhe and Vig, Amir},
  booktitle    = {arXiv},
  keywords     = {Differential Geometry (math.DG), Mathematical Physics (math-ph), Dynamical Systems (math.DS), Spectral Theory (math.SP), FOS: Mathematics, FOS: Mathematics, FOS: Physical sciences, FOS: Physical sciences, 58J42, 37J35, 37J35, 35P20, 58J40, 58J50, 37D40},
  title        = {{Spectral rigidity of Liouville tori}},
  doi          = {10.48550/ARXIV.2511.10398},
  year         = {2025},
}

@article{17203,
  abstract     = {The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found.

In this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes.

This insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.},
  author       = {Hafner, Christian and Ly, Mickaël and Wojtan, Christopher J},
  issn         = {1557-7368},
  journal      = {Transactions on Graphics},
  keywords     = {Topology Optimization, Mass Moments, Computational Geometry},
  location     = {Denver, Colorado},
  number       = {4},
  publisher    = {Association for Computing Machinery},
  title        = {{Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments}},
  doi          = {10.1145/3658194},
  volume       = {43},
  year         = {2024},
}

@phdthesis{18443,
  abstract     = {In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between
the hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they
conjecture an equivalence between categories of BBB and BAA-branes. At the classical
level, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on
algebraic integrable systems.
In this thesis, we investigate the T-duality relation between hyperkähler structures and the
corresponding branes on affine torus bundles. We use the techniques of generalized geometry
to show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.
We also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform
we upgrade the T-duality between generalized branes to T-duality of submanifolds endowed
with U(1)-bundles and connections. This T-duality in the appropriate context specializes to
T-duality between BBB and BAA-branes.
},
  author       = {Sisak, Maria A},
  issn         = {2663-337X},
  keywords     = {hyperkaehler geometry, branes, mirror symmetry, T-duality},
  pages        = {178},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{T-dual branes on hyperkähler manifolds}},
  doi          = {10.15479/at:ista:18443},
  year         = {2024},
}

@article{12287,
  abstract     = {We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.},
  author       = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit and Wintraecken, Mathijs},
  issn         = {1432-0444},
  journal      = {Discrete & Computational Geometry},
  keywords     = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science},
  pages        = {156--191},
  publisher    = {Springer Nature},
  title        = {{Local criteria for triangulating general manifolds}},
  doi          = {10.1007/s00454-022-00431-7},
  volume       = {69},
  year         = {2023},
}

@article{14192,
  abstract     = {For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.},
  author       = {Lampart, Jonas and Mitrouskas, David Johannes and Mysliwy, Krzysztof},
  issn         = {1572-9656},
  journal      = {Mathematical Physics, Analysis and Geometry},
  keywords     = {Geometry and Topology, Mathematical Physics},
  number       = {3},
  publisher    = {Springer Nature},
  title        = {{On the global minimum of the energy–momentum relation for the polaron}},
  doi          = {10.1007/s11040-023-09460-x},
  volume       = {26},
  year         = {2023},
}

@article{14499,
  abstract     = {An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables.

The proof proceeds via an ‘additive structure’ dichotomy on the degree sequence and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics and low-rank approximation. In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright theorem on small-ball probability for polynomials of Gaussians, which we believe is of independent interest. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős reiterated in several of his open problem collections and for which he offered one of his notorious monetary prizes.},
  author       = {Kwan, Matthew Alan and Sah, Ashwin and Sauermann, Lisa and Sawhney, Mehtaab},
  issn         = {2050-5086},
  journal      = {Forum of Mathematics, Pi},
  keywords     = {Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Analysis},
  publisher    = {Cambridge University Press},
  title        = {{Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture}},
  doi          = {10.1017/fmp.2023.17},
  volume       = {11},
  year         = {2023},
}

@article{14756,
  abstract     = {We prove the r-spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer r: the 2-groupoid of 2-dimensional fully extended r-spin TQFTs with given target is equivalent to the homotopy fixed points of an induced Spin 2r -action. In particular, such TQFTs are classified by fully dualisable objects together with a trivialisation of the rth power of their Serre automorphisms. For r=1, we recover the oriented case (on which our proof builds), while ordinary spin structures correspond to r=2.
To construct examples, we explicitly describe Spin 2r​-homotopy fixed points in the equivariant completion of any symmetric monoidal 2-category. We also show that every object in a 2-category of Landau–Ginzburg models gives rise to fully extended spin TQFTs and that half of these do not factor through the oriented bordism 2-category.},
  author       = {Carqueville, Nils and Szegedy, Lorant},
  issn         = {1663-487X},
  journal      = {Quantum Topology},
  keywords     = {Geometry and Topology, Mathematical Physics},
  number       = {3},
  pages        = {467--532},
  publisher    = {EMS Press},
  title        = {{Fully extended r-spin TQFTs}},
  doi          = {10.4171/qt/193},
  volume       = {14},
  year         = {2023},
}

@article{13049,
  abstract     = {We propose a computational design approach for covering a surface with individually addressable RGB LEDs, effectively forming a low-resolution surface screen. To achieve a low-cost and scalable approach, we propose creating designs from flat PCB panels bent in-place along the surface of a 3D printed core. Working with standard rigid PCBs enables the use of
established PCB manufacturing services, allowing the fabrication of designs with several hundred LEDs. 
Our approach optimizes the PCB geometry for folding, and then jointly optimizes the LED packing, circuit and routing, solving a challenging layout problem under strict manufacturing requirements. Unlike paper, PCBs cannot bend beyond a certain point without breaking. Therefore, we introduce parametric cut patterns acting as hinges, designed to allow bending while remaining compact. To tackle the joint optimization of placement, circuit and routing, we propose a specialized algorithm that splits the global problem into one sub-problem per triangle, which is then individually solved.
Our technique generates PCB blueprints in a completely automated way. After being fabricated by a PCB manufacturing service, the boards are bent and glued by the user onto the 3D printed support. We demonstrate our technique on a range of physical models and virtual examples, creating intricate surface light patterns from hundreds of LEDs.},
  author       = {Freire, Marco and Bhargava, Manas and Schreck, Camille and Hugron, Pierre-Alexandre and Bickel, Bernd and Lefebvre, Sylvain},
  issn         = {1557-7368},
  journal      = {Transactions on Graphics},
  keywords     = {PCB design and layout, Mesh geometry models},
  location     = {Los Angeles, CA, United States},
  number       = {4},
  publisher    = {Association for Computing Machinery},
  title        = {{PCBend: Light up your 3D shapes with foldable circuit boards}},
  doi          = {10.1145/3592411},
  volume       = {42},
  year         = {2023},
}

@article{13188,
  abstract     = {The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions, and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length.
We also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods, and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics.},
  author       = {Hafner, Christian and Bickel, Bernd},
  issn         = {1557-7368},
  journal      = {ACM Transactions on Graphics},
  keywords     = {Computer Graphics, Computational Design, Computational Geometry, Shape Modeling},
  number       = {5},
  publisher    = {Association for Computing Machinery},
  title        = {{The design space of Kirchhoff rods}},
  doi          = {10.1145/3606033},
  volume       = {42},
  year         = {2023},
}

@article{12129,
  abstract     = {Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P′ of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge (called edge flip), removes a non-extreme point of degree 3, or adds a point in P∖P′ as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The edge flip graph is defined with full triangulations as vertices, and edge flips determining the adjacencies. Lawson showed in the early seventies that these graphs are connected. The goal of this paper is to investigate the structure of these graphs, with emphasis on their vertex connectivity. For sets P of n points in the plane in general position, we show that the edge flip graph is ⌈n/2−2⌉-vertex connected, and the bistellar flip graph is (n−3)-vertex connected; both results are tight. The latter bound matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points to 3-space and projecting back the lower convex hull), where (n−3)-vertex connectivity has been known since the late eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky and Balinski’s Theorem. For the edge flip-graph, we additionally show that the vertex connectivity is at least as large as (and hence equal to) the minimum degree (i.e., the minimum number of flippable edges in any full triangulation), provided that n is large enough. Our methods also yield several other results: (i) The edge flip graph can be covered by graphs of polytopes of dimension ⌈n/2−2⌉ (products of associahedra) and the bistellar flip graph can be covered by graphs of polytopes of dimension n−3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n−3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations of a point set are regular iff the partial order of partial subdivisions has height n−3. (iv) There are arbitrarily large sets P with non-regular partial triangulations and such that every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular triangulations.},
  author       = {Wagner, Uli and Welzl, Emo},
  issn         = {1432-0444},
  journal      = {Discrete & Computational Geometry},
  keywords     = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science},
  number       = {4},
  pages        = {1227--1284},
  publisher    = {Springer Nature},
  title        = {{Connectivity of triangulation flip graphs in the plane}},
  doi          = {10.1007/s00454-022-00436-2},
  volume       = {68},
  year         = {2022},
}

@article{12148,
  abstract     = {We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  keywords     = {Computational Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Theoretical Computer Science, Analysis},
  publisher    = {Cambridge University Press},
  title        = {{Rank-uniform local law for Wigner matrices}},
  doi          = {10.1017/fms.2022.86},
  volume       = {10},
  year         = {2022},
}

@article{12216,
  abstract     = {Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments.},
  author       = {Carlen, Eric A. and Zhang, Haonan},
  issn         = {0024-3795},
  journal      = {Linear Algebra and its Applications},
  keywords     = {Discrete Mathematics and Combinatorics, Geometry and Topology, Numerical Analysis, Algebra and Number Theory},
  pages        = {289--310},
  publisher    = {Elsevier},
  title        = {{Monotonicity versions of Epstein's concavity theorem and related inequalities}},
  doi          = {10.1016/j.laa.2022.09.001},
  volume       = {654},
  year         = {2022},
}

@article{10588,
  abstract     = {We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.},
  author       = {Dello Schiavo, Lorenzo and Suzuki, Kohei},
  issn         = {1432-1807},
  journal      = {Mathematische Annalen},
  keywords     = {quasi curvature-dimension condition, sub-riemannian geometry, Sobolev-to-Lipschitz property, Varadhan short-time asymptotics},
  pages        = {1815--1832},
  publisher    = {Springer Nature},
  title        = {{Sobolev-to-Lipschitz property on QCD- spaces and applications}},
  doi          = {10.1007/s00208-021-02331-2},
  volume       = {384},
  year         = {2022},
}

@article{10643,
  abstract     = {We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.

},
  author       = {Henheik, Sven Joscha and Teufel, Stefan},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  keywords     = {computational mathematics, discrete mathematics and combinatorics, geometry and topology, mathematical physics, statistics and probability, algebra and number theory, theoretical computer science, analysis},
  publisher    = {Cambridge University Press},
  title        = {{Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk}},
  doi          = {10.1017/fms.2021.80},
  volume       = {10},
  year         = {2022},
}

@article{10623,
  abstract     = {We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.},
  author       = {Henheik, Sven Joscha},
  issn         = {1572-9656},
  journal      = {Mathematical Physics, Analysis and Geometry},
  keywords     = {geometry and topology, mathematical physics},
  number       = {1},
  publisher    = {Springer Nature},
  title        = {{The BCS critical temperature at high density}},
  doi          = {10.1007/s11040-021-09415-0},
  volume       = {25},
  year         = {2022},
}