Daniel Sage's home page

Daniel S. Sage
Department of Mathematics
Louisiana State University
Baton Rouge, LA 70806
USA
Email: sage at math dot lsu dot edu
Tel: (225) 578-1564 (W)
(225) 379-8675 (H)
FAX: (225) 578-4276

Education

Professional Experience

Research Interests

The geometric Langlands program
Geometric and combinatorial methods in representation theory
Hopf algebras and quantum groups
Composite materials and the G-closure problem

Selected Recent Talks

  • Diagrammatic and geometric approaches to Schur-Weyl duality, AMS Western Sectional Meeting, University of California Riverside, November 2019. Slides.
  • A tensor category structure on the equivariant perverse sheaves over matrices of bounded degree of nilpotency, AMS Eastern Sectional Meeting, University of Buffalo, September 2017. Slides.
  • Moduli spaces of connections, International Congress on Representations of Algebras (ICRA) 2016, Syracuse University, August 2016. Slides.
  • Moy-Prasad filtrations and flat G-bundles on curves, Geometric and Categorical Representation Theory, Mooloolaba, Australia, December 2015. Slides.
  • Minimal K-types for flat G-bundles, moduli spaces, and isomonodromy, 10th ISAAC Congress, Macau, China, August 2015. Slides.
  • Moy-Prasad filtrations and flat G-bundles on curves, Algebra Seminar, North Carolina State University, March 2015.
  • Moy-Prasad filtrations and flat G-bundles on curves, Working Group on Irregular Singularities, Mathematical Sciences Research Institute, December 2014.
  • Moduli spaces of flat G-bundles and isomonodromy, Workshop on Moduli Spaces of Connections, Centre Henri Lebesgue, Université de Rennes, July 2014. Slides.
  • Minimal K-types for flat G-bundles and moduli spaces}, lecture series (4 talks), Mini-workshop on Automorphic Forms and the Geometric Langlands Program, Fields Institute for Research in Mathematical Sciences, June 2014. Videos of the first three talks are available: Talk 1, Talk 2, Talk 3.

    Publications and Papers

    This is only a partial list.

  • Sage, D. S., A construction of representations of affine Weyl groups, Comp. Math., 108 (1997), 241--245.
  • Balaban, M. O., Sage, D. S., Smerage, G. H., Teixeira, A. A., and Welt, B. A., Iterative method for kinetic parameter estimation from dynamic thermal treatments, J. Food Science}, 62 (1997), 8--14.
  • Sage, D. S., The geometry of fixed point varieties on affine flag manifolds,Trans. Amer. Math. Soc., 352 (2000), 2087--2119.
  • Grabovsky, Y. and Sage, D. S., Exact relations for effective tensors of polycrystals. II: Applications to elasticity and piezo-electricity, Arch. Rat. Mech. Anal., 143 (1998), 331--356.
  • Grabovsky, Y., Milton, G. W. and Sage, D. S., Exact relations for effective tensors of polycrystals: Necessary conditions and sufficient conditions, Comm. Pure Appl. Math.,53 (2000), 300--353. Featured Review in Math Reviews.
  • Sage, D. S., Group actions on central simple algebras, Journal of Algebra, 250 (2002), 18-43.
  • Sage, D. S., Lie group actions on matrix algebras
  • Berger, K., Sage, D. S., and Welt, B., Performance specification of time-temperature integrators designed to protect against botulism in refrigerated fresh foods, Journal of Food Science, 68 (2003), 2--9.
  • Sage, D. S., Racah coefficients, subrepresentation semirings, and composite materials, Adv. App. Math., 34 (2005), 335--357.
  • Sage, D. S., Quantum Racah coefficients and subrepresentation semiring, J. Lie Theory, 15 (2005), 321--333.
  • Kwon, N. and Sage, D. S., Subrepresentation semirings and an analogue of 6j-coefficients, J. Math. Phys., 49 (2008), 063503.
  • Achar, P. N. and Sage, D. S., On special pieces, the Springer correspondence, and unipotent characters, Amer. J. Math., 130 (2008), 1399--1425.
  • Achar, P. N. and Sage, D. S., Perverse coherent sheaves and the geometry of special pieces in the unipotent variety, Adv. Math., 220 (2009), 1265--1296.
  • Achar, P. N. and Sage, D. S., Staggered sheaves on partial flag varieties, C. R. Acad. Sci. Paris, Ser. I, 347 (2009), 139--142.
  • Sage, D. S. and Smolinsky, L., An explicit basis of lowering operators for irreducible representations of unitary groups, Lith. J. Phys., 51 (2011), 5--18.
  • Sage, D. S. and Vega M., Twisted Frobenius-Schur indicators for Hopf algebras, J. Algebra, 354 (2012), 136--147.
  • Bremer, C. and Sage, D. S., Isomonodromic deformations of connections with singularities of parahoric formal type, Comm. Math. Phys., 313 (2012), 175--208.
  • Sage, D. S., Atomistic subsemirings of the lattice of subspaces of an algebra , Comm. Algebra, 41 (2013), 3652--3667.
  • Bremer, C. and Sage, D. S., Moduli spaces of irregular singular connections, Int. Math. Res. Not. IMRN, 2013 (2013), 1800--1872.
  • Bremer, C. and Sage, D. S., Generalized Serre conditions and perverse coherent sheaves , J. Algebra, 392 (2013), 85--96.
  • Sage, D. S. and Vega M., Twisted exponents and twisted Frobenius-Schur indicators for Hopf algebras, Comm. Algebra, 45 (2017), 9--16.
  • Bremer, C. and Sage, D. S., A theory of minimal K-types for flat G-bundles , Int. Math. Res. Not. IMRN, 2018 (2018), 3507--3555.
  • Bremer, C. and Sage, D. S., Flat G-bundles and regular strata for reductive groups , arXiv:1309.6060[math.AG], 2014.
  • Sage, D. S., Regular strata and moduli spaces of irregular singular connections , in New Trends in Analysis and Interdisciplinary Applications: Selected Contributions of the 10th ISAAC Congress, Macau 2015 (eds. P. Dang, M. Ku, T. Qian, L.~G. Rodino), 59--65. Trends in Mathematics, Birkhaüser/Springer, Cham, 2017.
  • Kamgarpour, M. and Sage, D. S., A geometric analogue of a conjecture of Gross and Reeder , Amer. J. Math, 141 (2019), 1457--1476.
  • Vogt, E., Sage, D. S., and Kjaergaard, H. G., Accuracy of XH-stretching intensities with the Deng-Fan potential, Molecular Phys., 117 (2018), 1629--1639.
  • Koroteev, P., Sage, D. S., and Zeitlin, A., (SL(N),q)-opers, the q-Langlands correspondence, and quantum/classical duality, arXiv:1811.09937[mathRT].
  • Kamgarpour, M. and Sage, D. S., Rigid connections on ℙ1 via the Bruhat-Tits building , arXiv:1910.00181[math.RT].
  • Frenkel, E., Koroteev, P., Sage, D. S., and Zeitlin, A., q-opers, QQ-systems, and Bethe ansatz, arXiv:2002:07344[mathAG].

    Teaching

    For more recent courses, see Moodle.
    Fall 2004
    MATH 2057-1 Multivariable Calculus III Syllabus Blackboard WeBWorK
    MATH 2057-2 Multivariable Calculus III Syllabus Blackboard WeBWorK
    Spring 2004
    MATH 1552-6 Analytic Geometry and Calculus II Syllabus
    MATH 1552-7 Analytic Geometry and Calculus II Syllabus
    Fall 2003
    MATH 2070-1 Mathematical Methods in Engineering Syllabus
    Spring 2003
    MATH 2090-4 Elementary Differential Equations and Linear AlgebraSyllabus
    MATH 2090-6 Elementary Differential Equations and Linear Algebra Syllabus

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