Doctor of Philosophy (Ph.D.)

Physics
University of Maryland, College Park
1987

Master of Science (M.Sc.) (not completed)

Physics
University of Zagreb, Yugoslavia (now Croatia)
1984

Bachelor of Science (B.Sc.)

Physics
University of Novi Sad, Yugoslavia (now Serbia)
1981

Mathematical Physics

Since 1983, Prof. Hübsch has pursued research at the forefront of high-energy and elementary particle physics as well as the related mathematics, such as algebraic geometry. This research includes (super)string theory, supersymmetric quantum field theory, related cosmology, and grand-unification model building on the physics side, and explicit construction of complex Ricci-flat (Calabi-Yau) spaces and the study of their structures and mirror symmetry on the mathematics side. His publication record is well catalogued at (Stanford University's) inSPIREhep database, the ORCID database, and the Google Scholar profile.BOOKS:Advanced Concepts in Particle and Field Theory(Cambridge University Press, Cambridge, 2015)Fizika elementarnih čestica (in Serbian language)(University of Novi Sad, Serbia, 2011)Calabi-Yau Manifolds: A Bestiary for Physicists(World Scientific, Singapore, 1992)

Elementary particle (high-energy) physics, quantum field theory, superstring theory

Selected publications (a baker's dozen):
• On de Sitter Spacetime and String Theory, P. Berglund, T. Hübsch and D. Minić: Int. J. Mod. Phys. D32 (2023) 2330002 (111 pp), arXiv:2212.06086
• On Stringy de Sitter Spacetimes, P. Berglund, T. Hübsch and D. Minić: J. High Energy Phys. 2019 (2019) 134950, arXiv:1902.08617
• A Generalized Construction of Calabi-Yau Models and Mirror Symmetry, P. Berglund and T. Hübsch: SciPost 4, 009 (2018) 1–30, arXiv:1611.10300
• Golden Ratio Controlled Chaos in Supersymmetric Dynamics, T. Hübsch and G.A. Katona: Int. J. Mod. Phys. A28 (2013) 1350156, arXiv:1308.0654
• A Superfield for Every Dash-Chromotopology, C.F. Doran, M.G. Faux, S.J. Gates, T. Hübsch, Jr., K.M. Iga and G.D. Landweber: Int. J. Mod. Phys. A24 (2009) 5681-5695, arXiv:0901.4970
• Localized Gravity and Large Hierarchy from String Theory ? P. Berglund, T. Hübsch and D. Minic: Phys. Lett. B512 (2001) 155-160, hep-th/0104057
• Gauging Yang-Mills Symmetries in 1+1-Dimensional Spacetime, Raja Q. Almukahhal and T. Hübsch: Int. J. Mod. Phys. A16 (2001) 4713-4768, hep-th/9910007
• Quantum Mechanics is Either Non-Linear or Non-Introspective, T. Hübsch: Mod. Phys. Lett. A13 (1998) 2503-2512; quant-th: 9712047
• A Generalized Construction of Mirror Manifolds, P. Berglund and T. Hübsch: Nucl. Phys. B393 (1993) 377-391; hep-th/9201014
• Rolling Among Calabi-Yau Vacua, P. Candelas, P. S. Green and T. Hübsch: Nucl. Phys. B330 (1990) 49-102
• Possible Phase Transitions Among Calabi-Yau Compactifications, P. Green and T. Hübsch: Phys. Rev. Lett. 61 (1988) 1163-1166
• Polynomial Deformations and Cohomology of Calabi-Yau Manifolds, P. Green and T. Hübsch: Commun. Math. Phys. 113 (1987) 505
• Calabi-Yau Manifolds - Motivations and Constructions, T. Hübsch: Commun. Math. Phys. 108 (1987) 291.

Group theory, supersymmetry, and algebraic geometry (as used in physics)

Selected publications (a baker's dozen):
• On Calabi-Yau generalized complete intersections from Hirzebruch varieties and novel K3-fibrations, P. Berglund and T. Hübsch: Adv. in Th. Math. Phys. 22 (2) (2018) 261–303, arXiv:1606.07420
• On General Off-Shell Representations of Worldline (1D) Supersymmetry, C.F. Doran, T. Hübsch, K.M. Iga and G.D. Landweber: Symmetry 6 no. 1, (2014) 67–88, arXiv:1310.3258
• Adinkra (In)Equivalence From Coxeter Group Representations: A Case Study, I. Chappell II, S.J. Gates, Jr. and T. Hübsch: Int. J. Mod. Phys. A29 no. 6, (2014) 1450029 (24p), arXiv:1210.0478
• Codes and Supersymmetry in One Dimension, C.F. Doran, M.G. Faux, S.J. Gates, Jr., T. Hübsch, K.M. Iga, G.D. Landweber and R.L. Miller: Adv. in Th. Math. Phys. 15 (2011) 1909-1970, arXiv:1108.4124
• ZN-Invariant Subgroups of Semi-Simple Lie Groups, M.K. Ahsan and T. Hübsch: J. Stat. Math. Sci. 2 (2016) 116, arXiv:1003.5823
• Off-shell supersymmetry and filtered Clifford supermodules, C.F. Doran, M.G. Faux, S.J. Gates, Jr., T. Hübsch, K.M. Iga and G.D. Landweber:  Algebras & Rep. Th. (July, 2017) 1–23, math-ph/0603012
• On the Geometry and Homology of Certain Simple Stratified Varieties, T. Hübsch and A. Rahman: J. of Geom. & Phys. 53/1 (2004) 31-48, math.AG/0210394
• A Fermionic Hodge Star Operator, A. Davis and T. Hübsch: Mod. Phys. Lett. A14 (1999) 965-976; hep-th/9809157
• On A Stringy Singular Cohomology, T. Hübsch: Mod. Phys. Lett. A12 (1997) 521-533; hep-th/9612075
• On A Residue Representation of Deformation, Chiral and Koszul Rings, P. Berglund and T. Hübsch: Int. J. Mod. Phys. A10 (1995) 3381-3430; hep-th/9411131
• An SL(2,C) Action on Chiral Rings and the Mirror Map, T. Hübsch and S.-T. Yau: Mod. Phys. Lett. A7 (1992) 3277-3289
• Connecting Moduli Spaces of Calabi-Yau Threefolds, P. Green and T. Hübsch: Comm. Math. Phys. 119 (1988) 431-441
• Invariants of Self-Adjoint Rank-Four SU(n) Tensors, T. Hübsch, S. Meljanac and S. Pallua: Phys. Rev. D32 (1985) 1021.  

Electromagnetic Theory

The goal of this 2-semester course is to provide a comprehensive and detailed treatment of electrostatic and magnetostatic configurations, Maxwell’s equations (and all the physics laws they encompass), and the response of dielectric and magnetic media to electromagnetic fields. Prerequisites to this course include electricity and magnetism at an advanced undergraduate level, and the working knowledge of vector calculus and orthogonal functions, such as those of the Bessel and Legendre and trigonometric type. The course also introduces the special theory of relativity stemming from the spacetime symmetries of Maxwell’s equations, resulting in the Lorentz-covariant formulation of electrodynamics, the interaction of the electromagnetic field with charged particles in motion. We then focus on specific configurations and arrangements, involving: (1) electromagnetic waves in nonconducting media, cavities and waveguides, (2) the multipole expansion of electromagnetic fields, radiation, scattering and diffraction, and various radiative processes. The course finishes with a brief review of electrodynamic feedback and the classical models of charged particles. See the syllabi for Semester 1 and Semester 2.

Math. Methods in Physics

This 2-semester course presents a review and practice of: (1) basic vector and tensor analysis, (2) ordinary and partial differential equations, (3) linear algebra and linear systems of algebraic and differential equarions (including eigenvalues & eigenvectors), (4) infinite series and products, (5) complex analysis (including residues), and (6) linear algebra. The focus is more on applications of the listed material than on proofs of the results, while maintaining mathematical rigor. We then introduce, develop and discuss various methods of solving first, second and higher order ordinary and partial differential equations subject to a variety of boundary, initial and final conditions. The emphasis is always on the adaptation of the standard mathematical methods and techniques to their application in solving typical problems in physics and engineering. Applications range from classical mechanics, hydrodynamics, electromagnetism and statistical physics through the quantum counterparts of these fields, and various engineering applications of these physics models, but also some less obviously related models such as variants of the predator-prey model in social economy and marketing. See the syllabi for Semester 1 and Semester 2.

Most Dissertations Advised for the Division of Engineering and Physical Sciences

(3 in the discipline of physics) for the year 2007–2008, 04/09/2009; Office of the Vice Provost for Research and Graduate School, Howard University

Outstanding Associate or Full Professor; 2017-18

Division of Natural Sciences, College of Arts and Sciences, Howard University

Advanced Concepts in Particle and Field Theory

Advanced Concepts in Particle and Field Theory

Designed for advanced undergraduates and graduate students and abounding in worked examples and detailed derivations, as well as including historical anecdotes and philosophical and methodological perspectives, this textbook provides students with a unified understanding of all matter at the fundamental level. Topics range from gauge principles, particle decay and scattering cross-sections, the Higgs mechanism and mass generation, to spacetime geometries and supersymmetry.

String Theory Bounds on the Cosmological Constant, the Higgs mass, and the Quark and Lepton Masses

String Theory Bounds on the Cosmological Constant, the Higgs mass, and the Quark and Lepton Masses

We elaborate on the new understanding of the cosmological constant and the gauge hierarchy problems in the context of string theory in its metastring formulation, based on the concepts of modular spacetime and Born geometry. The interplay of phase space (and Born geometry), the Bekenstein bound, the mixing between ultraviolet (UV) and infrared (IR) physics and modular invariance in string theory is emphasized. This new viewpoint is fundamentally rooted in quantum contextuality and not in statistical observer bias (anthropic principle). We also discuss the extension of this point of view to the problem of masses of quarks and leptons and their respective mixing matrices.

Triple Interference, Non-linear Talbot Effect and Gravitization of the Quantum

Triple Interference, Non-linear Talbot Effect and Gravitization of the Quantum

Recently we have discussed a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea of gravitizing the quantum. In this paper we elaborate on a specific test of this new approach to quantum gravity using triple interference in a varying gravitational field. Our discussion is driven by a profound analogy with recent triple-path interference experiments performed in the context of non-linear optics. We emphasize that the triple interference experiment in a varying gravitational field would deeply influence the present understanding of the kinematics of quantum gravity and quantum gravity phenomenology. We also discuss the non-linear Talbot effect as another striking phenomenological probe of gravitization of the geometry of quantum theory.

On de Sitter Spacetime and String Theory

On de Sitter Spacetime and String Theory

We review various aspects of de Sitter spacetime in string theory: its status as an effective field theory spacetime solution, its relation to the vacuum energy problem in string theory, its (global) holographic definition in terms of two entangled and non-canonical conformal field theories, as well as a realization of a realistic de Sitter universe endowed with the observed visible matter and the necessary dark sector in order to reproduce the realistic cosmological structure. In particular, based on the new insight regarding the cosmological constant problem in string theory, we argue that in a doubled, T-duality-symmetric, phase-space-like and non-commutative generalized-geometric formulation, string theory can naturally lead to a small and positive cosmological constant that is radiatively stable and technically natural. Such a formulation is fundamentally based on a quantum spacetime, but in an effective spacetime description of this general formulation of string theory, the curvature of the dual spacetime is the cosmological constant of the observed spacetime, while the size of the dual spacetime is the gravitational constant of the same observed spacetime. Also, the three scales associated with intrinsic non-commutativity of string theory, the cosmological constant scale and the Planck scale, as well as the Higgs scale, can be arranged to satisfy various seesaw-like formulae. Along the way, we show that these new features of string theory can be implemented in a particular deformation of cosmic-string-like models.

Machine Learned Calabi-Yau Metrics and Curvature

Machine Learned Calabi-Yau Metrics and Curvature

Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric within a given Kähler class. In this paper we investigate numerical Ricci-flat metrics over smooth and singular K3 surfaces and Calabi-Yau threefolds. Using these Ricci-flat metric approximations for the Cefalú family of quartic twofolds and the Dwork family of quintic threefolds, we study characteristic forms on these geometries. We observe that the numerical stability of the numerically computed topological characteristic is heavily influenced by the choice of the neural network model, in particular, we briefly discuss a different neural network model, namely Spectral networks, which correctly approximate the topological characteristic of a Calabi-Yau. Using persistent homology, we show that high curvature regions of the manifolds form clusters near the singular points. For our neural network approximations, we observe a Bogomolov--Yau type inequality 3c2≥c21 and observe an identity when our geometries have isolated A1type singularities. We sketch a proof that χ(X ∖ SingX)+2 |SingX|=24 also holds for our numerical approximations.