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Previous work of Chan--Church--Grochow and Baker--Wang shows that the set of spanning trees in a plane graph $G$ is naturally a torsor for the Jacobian group of $G$. Informally, this means that the set of spanning trees of $G$ naturally forms a group, except that there is no distinguished identity element. We generalize this fact to graphs embedded on orientable surfaces of arbitrary genus, which can be identified with ribbon graphs. In this generalization, the set of spanning trees of $G$ is replaced by the set of spanning quasi-trees of the ribbon graph, and the Jacobian group of $G$ is replaced by the Jacobian group of the associated regular orthogonal matroid $M$ (along with an associated regular representation of $M$). Our proof shows, more generally, that the family of "BBY torsors" constructed by Backman--Baker--Yuen and later generalized by Ding admit natural generalizations to (regular representations of) regular orthogonal matroids. In addition to shedding light on the role of planarity in the earlier work mentioned above, our results represent one of the first substantial applications of orthogonal matroids (also called "even delta-matroids" or "Lagrangian orthogonal matroids") to a natural combinatorial problem about graphs.

For a non-zero parameter $q$, we define Hermite trace polynomials, which are multivariate polynomials indexed by permutations. We prove several combinatorial properties for them, such as expansions and product formulas. The linear functional determined by these trace polynomials is a state for $q = \frac{1}{N}$ for $N$ a non-zero integer. For such $q$, Hermite trace polynomials of different degrees are orthogonal. The product formulas extend to the closure with respect to the state. The state can be identified with the expectation induced by the $N \times N$ Hermitian Brownian motion. Hermite trace polynomials are martingales for this Brownian motion, while the elements in the closure can be interpreted as stochastic integrals with respect to it. Using the grading on the algebra, we prove several chaos decompositions for such integrals, as well as analyze corresponding creation and annihilation operators. In the univariate, pure trace polynomial case, trace Hermite polynomials can be identified with the Hermite polynomials of matrix argument.

The sparse analogue of Szemerédi's regularity method has played a central role in the development of extremal results for random graphs. While the sparse embedding lemma (the KLR conjecture) has been resolved, the corresponding sparse counting lemma remains widely open. The conjecture, formulated by Gerke, Marciniszyn, and Steger, states that for every fixed graph $H$ and any $β>0$, there exists $\varepsilon>0$ such that the following holds. Consider a balanced blow-up of $H$ with vertex classes of size $n$, where each pair corresponding to an edge of $H$ forms an $(\varepsilon)$-regular bipartite graph with exactly $m$ edges. Assume that $m$ is above the natural threshold $m \gg n^{2-1/m_2(H)}$, then all but a $β^m$ proportion of such graphs contain at least $(1-δ)$ times the expected number of copies of $H$. In this paper, we establish the $H=K_4$ case of the conjecture.

We develop the theory of transfer and norm maps for finite group schemes, extending classical results from finite group theory to a context where induction and restriction are not necessarily bi-adjoint. In the additive setting, we construct a transfer map for both modules and $\rm Ext $ groups and prove that its surjectivity characterizes relative projectivity, establishing a generalization of Higman's criterion. In the multiplicative setting, we define a relative norm map for algebras with a group scheme action. We compare this norm with other versions in the literature, proving that it coincides with Mumford's norm for finite morphisms and on fields is a power of the classical field norm.

This manuscript contains preprint of a chapter under consideration for inclusion in the forthcoming third edition of {\em Cover and Thomas's Elements of Information Theory}, posted with permission from Wiley. The table of contents EIT-3 ToC of the new edition can be found at: https://docs.google.com/document/d/1L-m4oQEJw1PJhoxBeMwrrBD8S_HmvzMEkPbYvS24980/edit?usp=sharing . For feedback, please contact abbas@ee.stanford.edu Learning and information theory intersect in both model training and the characterization of fundamental performance limits. This manuscript provides a concise and accessible treatment of the first intersection, requiring only basic background in information theory and statistics at the senior undergraduate or first-year graduate level. End-of-chapter exercises make the material well suited for classroom use as well as self-study. The chapter focuses on the role of divergence measures in model training, with examples ranging from linear and logistic regression to autoregressive models, variational autoencoders, diffusion models, generative adversarial networks, and score-based models. It introduces the evidence lower bound (ELBO), f-divergences, and the Fisher divergence. In particular, the treatment of the generative diffusion model provides a more systematic and explicit derivation than is typical in the literature.

We construct the Higgs and Yukawa sectors as a structural completion of an algebraic three-generation model based on the complex Clifford algebra $\mathbb{C}\ell(10)$ with an intrinsic $S_3$ family symmetry. This addresses a common limitation of algebraic frameworks, in which Standard Model fermion multiplets and gauge symmetries may be described naturally, while the Higgs and Yukawa sectors remain less developed or absent. In the present framework, three algebraically distinguished fermion sectors are permuted by $S_3$, while the Standard Model gauge generators remain generation-independent. Higgs components are realised as right-action operators mapping weak-doublet fermion sectors into the corresponding weak-singlet sectors, and Yukawa coefficients are extracted using a Hilbert--Schmidt trace pairing. This yields two first-generation Higgs doublets with electroweak quantum numbers $(1,2,-1)$ and $(1,2,+1)$ under $SU(3)_C \times SU(2)_L \times U(1)_Y$, together with a Type-II-like separation between down-type and up-type Yukawa channels. Acting with the order-three family generator then generates a family-resolved Higgs sector organised into cyclic $S_3$ orbits. In the cyclically averaged Higgs limit, the Type-II-like Yukawa selection rule is preserved, while the generation-space Yukawa matrix is fixed algebraically and is non-diagonal in the algebraic generation basis. Under the usual implementation of electroweak symmetry breaking, the neutral Higgs couplings are aligned with the corresponding mass matrices, so tree-level flavour-changing neutral currents are not expected in this limit. The result is a constrained algebraic starting point for future $S_3$-breaking flavour phenomenology.

Let $β$ be a non-unit real algebraic integer greater than one and $\{a_{n}\}_{n \geq 0}$ be a sequence satisfying a linear recurrence relation $a_{n+3}=aa_{n+2}+ba_{n+1}+ca_{n}$. Under certain conditions, we prove that the number of $a_{n}$ which are palindromic concatenations of two repdigits in base $β$ is finite.

We investigate Diophantine pairs and triples of triangular numbers with the property $D(a)$ for a non-zero integer $a$. We prove that if a triangular number belongs to a $D(a)$-pair, it can be extended to infinitely many $D(a)$-triples of triangular numbers. Additionally, we determine infinite families of integers $a$ that admit such pairs, as well as families for which no $D(a)$-pairs can exist.

Cut-diagrams are diagrammatic objects, defined in dimensions 1 and 2, that generalize links in 3-space and surface-links in 4-space; in dimension 1, this coincides with the theory of welded links. Using cut-diagrams, we introduce an equivalence relation called cut-concordance, which encompasses the topological notion of concordance for classical links. Our main result is that the nilpotent peripheral system of 1-dimensional cut-diagrams is an invariant of cut-concordance, giving along the way a combinatorial version of a theorem of Stallings. We also investigate the relationship with several other equivalence relations in diagrammatic knot theory, in particular in connection with link-homotopy.

Folkman's theorem asserts the existence of graphs $G$ which are $K_4$-free, but which have the property that every two-coloring of $E(G)$ contains a monochromatic triangle. The quantitative aspects of $f(2,3,4)$, the least $n$ such that there exists an $n$-vertex graph with both properties above, are notoriously difficult; a series of improvements over the span of two decades witnessed the solution to two \$100 Erdős problems, and the current record due to Lange, Radziszowski, and Xu now stands at $f(2,3,4) \leq 786$,with another \$100 problem of Graham asking for a proof that $f(2,3,4) < 100$. In this paper, we study Folkman-like properties of a sequence $H_q$ of finite geometric graphs constructed using Hermitian unitals in projective planes and present some evidence that the graph $H_3$, which has 63 vertices, might contain a Folkman graph as a proper subgraph. More precisely, we first prove that for all prime powers $q \geq 3$, there exists a system $\mathscr{T}_q$ of triangles in $H_q$ such that no four span a $K_4$ in $H_q$, but every two-coloring of $E(H_q)$ induces a monochromatic triangle in $\mathscr{T}_q$. We then show that a certain random alteration of $H_q$ which destroys all of its $K_4$'s will, for large $q$, maintain the Ramsey property with high probability.

We study universality of Lipschitz quotients. First, we modify a construction of Johnson, Lindenstrauss, Preiss and Schechtman to obtain a complete separable metric space that has every complete separable metric space as a Lipschitz quotient. Our main result is in the compact setting, where we prove that no such universal metric space can exist. We deduce this impossibility result by studying the curve-flat index, an ordinal index which provides a measure of the complexity of the curve-fragment structure in a metric space. We show that Lipschitz quotients cannot increase this index in compact domains; while there exist compact spaces with arbitrarily high countable curve-flat index. The main technical part of the paper is dedicated to proving a strong version of the latter fact: for every ordinal $α$ and every compact metric space $M$, there exists a compact metric space $N$ such that the curve-flat quotient of $N$ of order $α$ is almost-isometric to $M$.

Steinitz's theorem states that if a point $a \in \mathrm{int\,conv\,} X$ for a set $X \subset \mathbb{R}^d$, then $X$ contains a subset $Y$ of size at most $2d$ such that $a \in \mathrm{int\,conv\,}Y$. The bound $2d$ is best possible here. We prove the colourful version of this theorem and characterize the cases when exactly $2d$ sets are needed.

This work presents the design and performance characterization of the optical calibration systems produced for the Pacific Ocean Neutrino Experiment (P-ONE), which target gain, energy and time calibration in the detector. These systems include novel light-pulse driver circuitry based on gallium nitride field-effect transistor technology and its application to directional and isotropic, self-monitoring optical calibration instruments. A total of 330 directional light pulsers and two isotropic, 17-inch calibration modules (P-CALs) were produced for the first P-ONE line. We present the designs and performance of both the directional and isotropic calibration devices and perform detailed optical characterizations of both full-production batches. In a wavelength range of $365 - 520\,$nm, our developed driver circuits achieve emission intensities up to $10^{11}\,$photons and pulse widths as small as $1.4\,$ns, respectively. Light-pulse drivers and self-monitoring electronics in the P-CAL were characterized using the same experimental setup, and the instrument's optical-isotropy design was optimized in combination with a dedicated GEANT4-based simulation framework. The optimized P-CAL achieves a simulated isotropy grade of $1.00 \pm 0.01$ across the entire $4π\,$solid angle range. These simulation investigations were explicitly confirmed by dedicated measurements in both air and water using two independent experimental setups, and we report the results. With this, a detailed performance estimate for deployed P-CAL modules in P-ONE was possible.

Let $E/\mathbb{Q}$ be an elliptic curve and let $ρ_E \colon \operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \to \operatorname{GL}(2, \widehat{\mathbb{Z}})$ be the adelic Galois representation attached to $E$. Much work has been done in recent years to study the image of $ρ_E$ (up to conjugation) as part of Mazur's so called ``Program B.'' In this paper, we describe and implement an efficient algorithm to compute the image of $ρ_E$ in $\operatorname{GL}(2, \widehat{\mathbb{Z}})$ (up to conjugation) for an elliptic curve $E/\mathbb{Q}$ with complex multiplication (CM) and $j$-invariant not $0$ or $1728$.

This letter presents a novel approach for \mbox{efficiently} computing time-index powered weighted sums of the form $\sum_{n=0}^{N-1} n^{K} v[n]$ using cascaded accumulators. Traditional direct computation requires $K{\times}N$ general multiplications, which become prohibitive for large $N$, while alternative strategies based on lookup tables or signal reversal require storing entire data blocks. By exploiting accumulator properties, the proposed method eliminates the need for such storage and reduces the multiplicative cost to only $K{+}1$ constant multiplications, enabling efficient real-time implementation. The approach is particularly useful when such sums need to be efficiently computed in sample-by-sample processing systems.

Solid-state scintillators are widely used in particle and applied physics due to their versatility and resistance to diverse environments and operating conditions. This broad range of applications calls for thorough characterization of scintillating crystals. Among these materials, cerium-doped yttrium aluminum garnet (YAG:Ce) is a promising scintillator owing to its favorable timing characteristics, high light yield, good mechanical properties, and chemical stability. In this work, we report a comprehensive experimental characterization of a YAG:Ce crystal exposed to both $γ$ and $alpha$ radiation. We extract the scintillation decay time and light yield, and study their evolution from room temperature down to approximately $-50 ^\circ$ C. We perform a detailed investigation of the quenching factor for \al particles in the energy range from about $6$ MeV down to $1$ MeV, finding a value that decreases from approximately $0.17$ to $0.10$. We also explore the possibility of pulse-shape discrimination based on the different signal evolution depending on the interaction type, demonstrating strong classification capabilities. These results provide a detailed assessment of the performance of \YAG for radiation-detection applications and offer insight into its potential use in environments requiring reliable particle identification and stable response across a wide range of operating conditions.

A persistence diagram is a finite multiset of birth-death pairs representing the lifetimes of topological features across a filtration. Existing functional and kernel representations of persistence diagrams are typically constructed extrinsically through embeddings into auxiliary spaces. For filtrations with finite indexing sets, the associated virtual persistence diagram group obtained by Grothendieck completion of the persistence diagram monoid is a finitely generated lattice. We define a phase map sending each persistence interval to a circular coordinate and a character map aggregating the phases of intervals in a virtual persistence diagram. We introduce heat damping on characters of virtual persistence diagram groups to suppress the unstable frequencies. We derive Lipschitz bounds for the resulting kernels and apply them in a synthetic segmentation experiment.

We revisit size controllability results in Pötscher and Preinerstorfer (2025) concerning heteroskedasticity robust test statistics in regression models. For the special, but important, case of testing a single restriction (e.g., a zero restriction on a single coefficient), we povide a necessary and sufficient condition for size controllability, whereas the condition in Pötscher and Preinerstorfer (2025) is, in general, only sufficient (even in the case of testing a single restriction).

We study a Navier-Stokes/Cahn-Hilliard system modeling the evolution of a compressible binary mixture of viscous fluids undergoing phase separation. The novelty of this work is a free energy potential including the physically relevant Flory-Huggins (logarithmic) entropy, as opposed to previous studies in the literature, which only consider regular potentials with polynomial growth. Our main result establishes the existence of global-in-time weak solutions in three-dimensional bounded domains for arbitrarily large initial data. The core contribution is the derivation of new estimates for the chemical potential and the Flory-Huggins entropy arising from a density-dependent Cahn-Hilliard equation under minimal assumptions: non-negative $γ$-integrable density with $γ>\frac32$. In addition, we prove that the phase variable, which represents the difference of the mass concentrations, takes value within the physical interval $(-1,1)$ almost everywhere on the set where the density is positive.

We present a quantum preconditioning framework for solving linear systems arising from a finite difference discretization of the Poisson equation. It is based on the combination of the Schrödingerization technique \cite{JLY22b,JLYPRL24} and the BPX multilevel preconditioner in order to achieve near-optimal complexity. The Schrödingerization technique transforms linear partial and ordinary differential equations into Schrödinger-type systems with unitary evolution in one higher dimension, making them suitable for quantum simulation. A key contribution is a structure-aware construction of the block-encoding for the symmetrically preconditioned matrix $A_S = S^\top A S$, where $A$ is the stiffness matrix and $S$ encodes the BPX preconditioner in factored form. By establishing a novel commuting identity, we avoid the unfavorable normalization scaling that would otherwise arise from naive multiplication of block-encodings. This yields an exact block-encoding of $A_S$ with normalization $\mathcal{O}(d^2(L+1))$, where $d$ is the spatial dimension and $L$ is the number of levels. Combined with the Schrödingerization-based Hamiltonian simulation, the overall quantum algorithm achieves a query complexity of $\mathcal{O}\big(\mathrm{poly}(d)\varepsilon^{-1} \mathrm{polylog}(\varepsilon^{-1}) \big)$ for estimating linear functionals of the solution to a given tolerance $\varepsilon$.

Answering a question of Goode, we show that $k$-triviality collapses to (1-)triviality among simple theories. In particular, every stable theory with quantifier elimination in a relational language of bounded arity is trivial. We use our collapse result, along with other facts about $k$-triviality and $k$-total triviality, to generate examples of (strongly) $k$-distal theories. The collapse result immediately implies that no stable theory can be strictly $k$-distal for some $k\geq 3$, partially answering a question of Walker. Moreover, all known examples of non-distal (strongly) $k$-distal theories are $k$-ary, rendering (strong) $k$-distality moot as a $(k+1)$-ary dividing line; we give four classes of examples that are not $k$-ary. We also show that just as distality is not preserved under taking reducts, neither is (strong) $k$-distality.

We study phase transitions on dynamic triadic hypergraphs, in which a continuous formation field evolves under stochastic Ginzburg--Landau dynamics with a cubic three-body coupling $g_τϕ_iϕ_jϕ_k$, while a discrete opinion variable $s_i\in\{-1,+1\}$ undergoes Kawasaki exchange under a Hamiltonian with pairwise alignment and an irreducible three-body energy $-λ_τ\prod_{a\inτ}s_a$. Near the formation critical point the cubic coupling is subleading and the transition remains continuous, controlled at leading order by a pairwise Ising baseline with renormalized coupling $J_{\rm eff}=J+γw$. The dominant observable is the triadic formation correlator $Ψ_{\rm form}\equiv\langleϕ_iϕ_jϕ_k\rangle$, a $k=3$ composite operator built over the underlying $\mathbb{Z}_2$-symmetric order parameter. Composite-operator scaling yields the effective exponents $β_{\rm TF}=3/2$ and $γ_{\rm TF}=-1$. The susceptibility conjugate to $Ψ_{\rm form}$ vanishes at the critical temperature $T_c$ rather than diverging, in contrast to the divergence characterizing scalar (pairwise) order parameters. The exact partition function of the minimal triad on $\{-1,+1\}^3$ identifies a crossover scale $T^*=4J_{\rm eff}/\ln 3$. A field-theoretic two-point function argument reproduces the same vanishing susceptibility. Restoring the three-body coupling ($λ\neq0$) makes the transition first-order, with a critical endpoint at $λ=0$. The exponent relations $β_{\rm TF}=3β_{\rm Ising}$ and $γ_{\rm TF}=γ_{\rm Ising}-4β_{\rm Ising}$ hold exactly on dense hypergraphs via cluster decomposition, and the vanishing-susceptibility signature persists for $d\geq3$ but fails in $d=2$. A Mori--Zwanzig memory kernel yields a continuously tunable dynamical exponent $z_{\rm TF}$, completing the composite-operator scaling regime.

Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model with data-driven methods such as machine learning emulators. While emulators are promising tools for accelerating simulations and solving inverse problems, they still struggle to learn chaotic dynamics, where sensitivity to initial conditions renders exact long-term forecasts infeasible, especially given noisy data. Recent work instead trains emulators to match the statistical properties of chaotic attractors, but these approaches often rely on handcrafted summary statistics or large, diverse multi-environment datasets. In this work, we propose a family of adversarial optimal transport objectives that can jointly learn high-quality summary statistics and a physically consistent emulator from a single noisy trajectory. We theoretically analyze and experimentally validate a Sinkhorn divergence formulation (2-Wasserstein) and a WGAN-style dual formulation (1-Wasserstein) of our approach. Numerical experiments across a variety of chaotic systems, including ones with high-dimensional spatiotemporal chaos, show that emulators trained using our proposed objectives have significantly improved long-term statistical fidelity.

In this work, we investigate the non-equilibrium dynamics in a one-dimensional two-component anyon-Hubbard model, which can be mapped to an extended Bose-Hubbard ladder with density-dependent hopping phase and synthetic gauge flux. Through numerical simulations of two-particle dynamics and the symmetry analysis, we reveal the asymmetric transport with broken inversion symmetry and two dynamical symmetries in the expansion dynamics. The expansion of two-component anyons is dynamically symmetric under spatial inversion and component flip, when the sign of anyonic statistics phase or the signs of gauge flux and interaction are changed. In the non-interacting case, we show the dynamical suppression induced by both the statistics phase and gauge flux. In the interacting case, we demonstrate that both chiral and antichiral dynamics can be exhibited and tuned by the statistics phase and gauge flux. The dynamical phase regimes with respect to the chiral-antichiral dynamics are obtained. These findings highlight the rich dynamical phenomena arising from the interplay of anyonic exchange statistics, synthetic gauge fields, and interactions in multi-component anyons.

In 1977, Chung, Chung and Liu generalized the definition of the Ramsey number. They introduced the $s$-chromatic Ramsey number as follows. Let $1\leq s< t$ be integers and let $A_{1}, A_{2}, \dots, A_{c}$ be subsets with size $s$ of $[t]$, where $c= {t\choose s}$. For given graphs $G_{1}, G_{2}, \dots, G_{c}$, the {\it $s$-chromatic Ramsey number} $r^{s, t}(G_{1}, G_{2}, \dots, G_{c})$, is the minimum positive integer $N$ such that every $t$-coloring of $E(K_{N})$ yields a copy of $G_{i}$ whose edges are colored by colors in the color set $A_{i}$ for some $i\in [c]$. The {\it star-critical $s$-chromatic Ramsey number} $r_{*}^{s, t}(G_{1}, G_{2}, \dots, G_{c})$, is the minimum integer $\ell$ such that every $t$-coloring of the edges in $K_{N}- E(K_{1, N- 1- \ell})$ yields a copy of $G_{i}$ whose edges are colored by colors in the color set $A_{i}$ for some $i\in [c]$, where $N= r^{s, t}(G_{1}, G_{2}, \dots, G_{c})$. If $G_{1}= G_{2}= \dots= G_{c}= G$, then we simplify them to $r^{s, t}(G)$ (also called the {\it weakened Ramsey number}) and $r^{s, t}_{*}(G)$, respectively. In this paper, we determine all the values of $r^{s, t}(K_{1, m})$ and $r_{*}^{s, t}(K_{1, m})$, and part of the value of $r^{s, t}(K_{1, m_{1}}, K_{1, m_{2}}, \dots, K_{1, m_{c}})$.

Over an arbitrary field, we conduct a comprehensive study of the polynomial identities and codimensions of two- and three-dimensional metabelian non-Lie Leibniz algebras. In addition, we compute the images of multihomogeneous polynomials on two-dimensional Leibniz algebras and, as a consequence, prove that the image of any multilinear polynomial evaluated on such algebras is always a vector space. Our analysis includes the three nontrivial isomorphism classes in dimension two and the ten isomorphism classes in dimension three, all of which are metabelian. In particular, we determine finite bases for their corresponding $T$-ideals and provide explicit bases for the associated relatively free graded algebras.

The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal meromorphic bundles with algebraic structure group, and admitting no horizontal subvarieties, is deduced. Examples of algebraic groups arising as binding groups are provided, as is a characterisation of when they are linear. Using binding groups in CCM it is shown that, in contrast to the situation in differentially closed fields, there are many algebraic groups which admit nontrivial definable torsors over acl-closed sets in the theory DCCM of existentially closed differential CCM-structures. A self-contained exposition of the binding group theorem in totally transcendental theories, that emphasises the bitorsorial nature of the construction, is also included.

This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in a trivial tail $σ$algebra. A classical example known since the 1930's is that a time series is fully determined by its values on the negative integers if its spectrum has a gap, or at least a sufficiently deep zero. We extend such results to higher dimensions and continuous settings by establishing a connection with the concept of uniqueness pairs, rooted in the uncertainty principle of harmonic analysis. We present several other manifestations of this principle, unify and strengthen seemingly unrelated results across different models: quasicrystals and stealthy processes are shown to be maximally rigid on cones, and discrete integer-valued processes are necessarily periodic when they have a simply connected spectrum. Finally, we identify a surprising class of continuous fields with seemingly standard behavior, such as linear variance and finite dependency range, that undergo a phase transition: they are perfectly interpolable on B(0, $ρ$) for $ρ$ ___ 2 $π$ but exhibit no rigidity for $ρ$ > 2.

A fundamental property of Segre classes is their birational invariance. This invariance implies that the Segre class of a closed subscheme only depends on the integral closure of the defining ideal sheaf. In this paper, we show that, conversely, the Segre class of a closed subscheme encodes an integral dependence criterion for its defining ideal sheaf. As an application, we prove that Aluffi's Segre zeta function provides an integral dependence criterion for homogeneous ideals in polynomial rings.

In this paper we develop an algebraic theory to study the problem of finding the minimum distance point from an algebraic variety with respect to the Hermitian distance function. The theory generalizes the Euclidean Distance degree introduced in arXiv:1309.0049, replacing a positive symmetric bilinear form by a Hermitian form. Various examples are presented to show the robustness of the machinery.