Martin Gebert

University of California, Davis


I'm a Krener Assistant Professor at University of California, Davis working in analysis, spectral theory and operator theory. Before coming to Davis, I was at Queen Mary University of London, King's College London, briefly at ETH Zurich and LMU Munich.


MAT-127A (fall 2019)

MAT-017B (fall 2019)

MAT-127B (Spring 2019)

MAT-017A (Winter 2019)

MAT-017A (Fall 2018)


Have a look at ArXiv and MathSciNet.

[13] M.Gebert and C.Rojas-Molina, Lifshitz tails for the fractional Anderson model, preprint arXiv:1910.02077 (2019), submitted. ArXiv

[12] M.Gebert and M.Poplavskyi, On pure complex spectrum for truncations of random orthogonal matrices and Kac polynomials , preprint arXiv:1905.03154 (2019), submitted. ArXiv

[11] E.Fedele and M.Gebert, On determinants identity minus Hankel matrix, Bull. Lond. Math. Soc. 51, 751-764 (2019), ArXiv or Journal

[10] M.Gebert, A lower Wegner estimate and bounds on the spectral shift function for continuum random Schrödinger operators, J. Funct. Anal. 277, no. 11, 108284 (2019) ArXiv or Journal

[9] M.Gebert, On an integral formula for Fredholm determinants related to pairs of spectral projections, Integral Equations Operator Theory, 90:35 (2018). ArXiv or Journal

[8] A.Dietlein, M.Gebert and P.Müller, Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. J. Spectr. Theory 9, no. 3, 921–965 (2019). ArXiv or Journal

[7] A.Dietlein, M.Gebert, P.Hislop, A.Klein and P.Müller, A bound on the averaged spectral shift function and a lower bound on the density of states for random Schrödinger operators on ℝd, Int. Math. Res. Not. IMRN, 21, 6673--6697 (2018). ArXiv or Journal.

[6] M.Gebert and M.Lemm, On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field, J. Stat. Phys. 164, 667-679 (2016). ArXiv or Journal.

[5] M.Gebert, H.Küttler, P.Müller and P.Otte, The exponent in the orthogonality catastrophe for Fermi gases, J. Spectr. Theory 6, 643-683 (2016). ArXiv or Journal.

[4] M.Gebert, The asymptotics of an eigenfunction-correlation determinant for Dirac-delta perturbations, J. Math. Phys. 56, 072110-1-18 (2015). ArXiv or Journal.

[3] M.Gebert, Finite-size energy of non-interacting Fermi gases, Math. Phys. Anal. Geom. 18, 27-1-13 (2015). ArXiv or Journal.

[2] M.Gebert, H.Küttler and P. Müller, Anderson's orthogonality catastrophe, Commun. Math. Phys. 329, 979-998 (2014). ArXiv or Journal.

[1] M. Gebert and P. Müller, Localization for random block operators, Oper. Theory Adv. Appl. 232, 229-246 (2013). ArXiv or Journal.


Slides to some talks:

Overview of mathematics of Anderson's orthogonality and open problems: Talk held at Field's institue Toronto 2016. slides

Lower bound on density of states for continuum random Schrödinger operators: Talk held at CRM Montreal 2018. slides

Basic talk about persistence probability of truncated random orthogonal matrices: Talk held at GLaMP 2019. slides