Kathryn E. Hare

Contact information

Kathryn Hare

Department of Pure Mathematics 
University of Waterloo
Waterloo, Ontario, Canada
N2L 3G1

Email: kehare@uwaterloo.ca

Curriculum Vitae

Degrees

  • PhD (University of British Columbia) 1986

  • BMath (University of Waterloo) 1981

Awards

  • Fellow Canadian Mathematical Society, 2020

  • University of Waterloo, Mathematics Faculty Distinction in Teaching Award, 2020

  • Honourary Doctorate of Technology, Chalmers University of Technology, 2011

  • Female Guest Professor, Sweden, 2000-2001

  • AMS Featured Review, 1995

  • NSERC Postgraduate Scholarship, 1983-85

  • I.W. Killam Predoctoral Fellowship, 1985-86

  • NSERC Operating Grant, 1987-date

Academic appointments

Dates Position Institution
2018-2019 Visiting Professor Acadia University
2013-2014 Visiting Professor University of St. Andrews
2007-2008 Visiting Professor University of Hawaii-Manoa
Summer 2002 AARMS Workshop Instructor Memorial University
2000-2001 Visiting Professor Chalmers University of Technology and
Goteborg University
1996-Present Full Professor University of Waterloo
1991-96 Associate Professor University of Waterloo
1993-94 Visiting Fellow University of New South Wales
1988-91 Assistant Professor University of Waterloo
1986-88 Assistant Professor University of Alberta




University of Waterloo administrative appointments

Dates Position
2014-2018 Chair, Department of Pure Mathematics
2008-2012 Associate Chair for Graduate Affairs, Department of Pure Mathematics
2005 Associate Chair for Graduate Affairs, Department of Pure Mathematics
1999-2000 Associate Chair for Undergraduate Affairs, Department of Pure Mathematics
1994-1999 Associate Chair for Graduate Affairs, Department of Pure Mathematics




Selected External service

Dates Position
2005-date Mentor for Association for Women in Mathematics
2017 Local Organizer, CMS Winter Meeting
2016-date CMS Finance Committee
2016 External reviewer, graduate program, Western University
2012, 2014 Organising committee - Summer school for Women Undergraduates
2010-2012 Chair CMS Women in Math Committee
2009 External Reviewer, University of Regina Mathematics Department
2007-2012 Editor Canadian Math Bulletin & Canadian Journal of Math
2003-2005 Vice President Canadian Mathematics Society
2003-2005 CMS Endowment Funds Committee
2003-2005 CMS Education Committee
2003-2005 CMS Women in Math Committee
2003 External Reviewer, Dalhousie University Math Department
2002-2005 NSERC Grant Selection Committee for Mathematics
2002-2003 CMS Endowment Funds Committee. Chair
2002 Ontario Graduate Scholarship Panel
2002 NExTMAC Workshop Panelist
2001-2005 CMS Board of Directors
2001 External Reviewer, Memorial University Math Department
1999 CMS Endowment Funds Committee
1998-2000 Ontario Graduate Scholarship Panel. Chair in 1999
1998-1999 Chair, CMS Task Force on Support of the Mathematics Community
1997-1999 CMS Government Policy Committee
1997-1998 Organizing committee for first Canadian Celebration of Women in Mathematics
1992 Ministry of Education Workshop on secondary schools mathematics curriculum




Research papers

Papers in refereed journals

(a) Harmonic analysis on compact Lie groups

  • K. Hare and S. Gupta, Smoothness of convolutions of orbital measures on complex Grassmannians, accepted by J. Lie Theory.
  • K. Hare and S. Gupta, Transferring spherical multipliers on compact symmetric spaces, accepted by Math Zeitschrift.
  • K. Hare and J. He, Geometric proof of the L2 - singular dichotomy for orbital measures on Lie algebras and groups, Boll. Unione Mat. Ital. 11(2018), 573–580.
  • K. Hare and S. Gupta, The absolute continuity of convolutions of orbital measures in symmetric spaces, J. Math. Anal. and Appl. 450(2017), 81–111.
  • K. Hare and J. He, The absolute continuity of convolution products of orbital measures in symmetric spaces, Monatsh. Math. 182(2017), 619–635.
  • K. Hare and J. He, Smoothness of convolution products of orbital measures on rank one symmetric spaces, Bull. Aust. Math. Soc. 94(2016), 131–143.
  • K. Hare and S. Gupta, Characterizing the absolute continuity of the convolution of orbital measures in a classical Lie algebra, Can. J. Math. 68(2016), 841–874.
  • K. Hare, D. Johnstone, F. Shi and W-K. Yeung, L2-singular dichotomy for exceptional Lie groups and algebras, J. Aust. Math. Soc. 95(2013), 362–382.
  • S. Gupta and K. Hare, Smoothness of convolutions of zonal measures on compact, symmetric spaces, J. Math. Anal. Appl. 402 (2013), 668–678.
  • K. Hare and P. Skoufranis, The smoothness of orbital measures on exceptional Lie groups and algebras, J. Lie Theory 21 (2011), 987–1007.
  • S. Gupta and K. Hare, L2 - singular dichotomy for orbital measures on complex groups, Boll. Un. Math. Ital. (9) 3 (2010), 409–419.
  • S. Gupta and K. Hare, Smoothness of convolution powers of orbital measures on the symmetric spaces SU(n)/SO(n), Monat. Math. 159 (2010), 27–43.
  • S. Gupta and K. Hare, L2 - singular dichotomy for orbital measures of classical compact Lie groups, Adv. Math. 222 (2009), 1521–1573.
  • S. Gupta and K. Hare, Convolutions of generic orbital measures in compact symmetric spaces, Bull. Aust. Math. Soc. 79 (2009), 513–522.
  • S. Gupta, K. Hare and S. Seyfaddini, L2 - singular dichotomy for orbital measures of classical simple Lie algebras, Math. Zeit. 262 (2009), 91–124.
  • S. Gupta and K. Hare, Dichotomy problem for orbital measures of SU(n), Monatsch. Math., 146 (2005), 227–238.
  • K. Hare and K. Yeats, Size of characters of exceptional Lie groups, J. Aust. Math. Soc., 77 (2004), 1–16.
  • D. Grow and K. Hare, Independence of characters on non-abelian groups, Proc. Amer. Math. Soc., 132 (2004), 3641–3651.
  • K. Hare and W-L. Yee, The singularity of orbital measures on compact Lie groups, Rev. Iberoamericana, 20 (2004), 517–530.
  • S. Gupta and K. Hare, Singularity of orbits in classical Lie algebras, Geometric and Functional Analysis, 13 (2003), 815–844.
  • S. Gupta and K. Hare, Singularity of orbits in SU(n), Israel J., 130 (2002), 93–107.
  • K. Hare, D. Wilson and W-L. Yee, Pointwise estimates of the size of characters of compact Lie groups, J. Aust. Math. Soc., 69 (2000), 61–84.
  • K. Hare, The size of characters of compact Lie groups, Studia Math. 129 (1998), 1–18.

(b) Fractals and harmonic analysis

  • K. Hare and I. Garcia, Properties of quasi-Assouad, accepted by Ann. Acad. Sci. Fenn. Math.
  • K. Hare, I. Garcia and F. Mendivil, Intermediate Assouad-like dimensions, accepted by J. Fractal Geometry.
  • K. Hare, I. Garcia and F. Mendivil, Almost sure Assouad-like dimensions of complementary sets, accepted by Math. Zeitscrift.
  • K. Hare, K. G. Hare and W. Shen, The Lq spectrum for a class of self-similar measures with overlap, accepted by Asian J. Math.
  • K. Hare, K. G. Hare and A. Rutar, When the WSC implies the generalized FT condition, accepted by Proc. Amer. Math. Soc.
  • K. Hare and K. G. Hare, Intermediate Assouad-like dimensions for measures, accepted by Fractals.
  • K. Hare, C. Cabrelli and U. Molter, Riesz bases of exponentials and the Bohr topology, accepted by Proc. Amer. Math. Soc.
  • K. Hare and S. Troscheit, Lower Assouad dimension and regularity, accepted by Proc. Camb. Phil. Soc.
  • K. Hare, F. Mendivil and L. Zuberman, Measures with specified support and arbitrary Assouad dimension, Proc. Amer. Math. Soc. 184(2020), 3881–3895.
  • K. Hare, K. G. Hare and S. Troscheit, Quasi-doubling self-similar measures with overlaps, J Fractal Geometry, 7(2020), 233–270.
  • K. Hare, K. G. Hare, B. Morris and W. Shen, Entropy of Cantor-like measures, Acta. Math. Hung. 159(2019), 563–588.
  • K. Hare and K. G. Hare, Local dimensions of overlapping self-similar measures, Real Analysis Exch. 44(2019), 247–266.
  • K. Hare, J. Fraser, K. G. Hare, S. Troscheit and H. Yu, The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra, Ann. Acad. Fenn. 44(2019), 379–387.
  • K. Hare, K. G. Hare and K. Matthews, Local dimensions of measures of finite type on the torus, Asian. J. Math. 23(2019), 127–155.
  • K. Hare, K. G. Hare and S. Troscheit, Local dimensions of random honogeneous self-similar measures: strong separation and finite type, Math. Nach., 291(2018), 2397–2426.
  • K. Hare, K. G. Hare and M. Ng, Local dimensions of measures of finite type II - measures without full support and with non-regular probabilities, Can. J. MAth. 70(2018), 824–867.
  • K. Hare, I. Garcia and F. Mendivil, Assouad dimensions of complementary sets, Proc. Royal Soc. Edinburgh, 148A(2018), 517–540.
  • K. Hare, K. G. Hare and G. Simms, Local dimensions of measures of finite type III - measures that are not equicontractive, J. Math. Anal. and Appl. 458(2018), 1653–1677. Corr. J. Math. Anal. and Appl. 483(2020), 123550.
  • K. Hare, K. G. Hare and K. Matthews, Local dimensions of measures of finite type, J. Fractal Geometry, 2(2016), 331–376.
  • K. Hare, Self-affine measures that are Lp-improving, Colloq. Math. 139(2015), 299–243.
  • K. Hare, F. Mendivil and L. Zuberman, Packing and Hausdorff measures of Cantor sets associated with series, Real Anal. Exch. 40(2015), 421–433.
  • K. Hare and M. Ng, Hausdorff and packing measure of balanced Cantor sets, Real Anal. Exch. 40(2014), 113–128.
  • C. Bruggeman, C. Mak and K. Hare, Multifractal spectrum of self-similar measures with overlap, Nonlinearity 27 (2014), 227–256.
  • C. Bruggeman and K. Hare, Multi-fractal analysis of convolution powers of measures, Real Anal. Exch. 38 (2012/13), 391–408.
  • K. Hare, F. Mendevil and L. Zuberman, The sizes of rearrangements of Cantor sets, Can. Math. Bull. 56 (2013), 354–365.
  • K. Hare, B. Steinhurst, A. Teplyaev and D. Zhou, Disconnected Julia sets and gaps in the spectrum of Laplacians on symmetric finitely ramified fractals, Math. Res. Lett. 19 (2012), 537–553.
  • P-W. Fong, K. Hare and D. Johnstone, Multifractal analysis for convolutions of overlapping Cantor measures, Asian J. Math. 15 (2011), 53–69.
  • K. Hare and L. Zuberman, Classifying Cantor sets by their multifractal spectrum, Non-Linearity, 23 (2010), 2919–2933.
  • C. Cabrelli, K. Hare and U. Molter, Classifying Cantor sets by their fractal dimensions, Proc. Amer. Math. Soc., 138 (2010), 3965–3974.
  • K. Hare and D. Zhou, Gaps in the ratios of the spectrum of Laplacians on fractals, Fractals 17 (2009), 523–535.
  • K. Hare, P. Mohanty and M. Roginskaya, General energy formula, Math. Scand., 101 (2007), 29–47.
  • M. Allen, G. Cruttwell, J.-O. Ronning and K. Hare, Dimensions of fractals in the large, Chaos, Solitons and Fractals, 31 (2007), 5–13.
  • K. Hare and M. Roginskaya, Lp-Improving properties of measures of positive energy dimension, Colloq. Math., 102 (2005), 73–86.
  • K. Hare and M. Roginskaya, Energy of signed measures, Proc. Amer. Math. Soc., 132 (2004), 397–406.
  • K. Hare and J-O. Ronning, Fractal dimensions of infinite product spaces, Int. J. Pure & App. Math., 14 (2004), 136–169.
  • K. Hare and M. Roginskaya, Multipliers of spherical harmonics and energy of measures on the sphere, Arkiv. Mat., 41 (2003), 281–294.
  • K. Hare and M. Roginskaya, A Fourier series formula for energy of measures with applications to Riesz products, Proc. Amer. Math. Soc., 131 (2003), 165–174.
  • K. Hare and M. Roginskaya, Energy of measures on compact Riemannian manifolds, Studia Math., 159 (2003), 291–314.
  • C. Cabrelli, K. Hare and U. Molter, Sums of Cantor sets yielding an interval, J. Aust. Math. Soc., 73 (2002) 405–418.
  • K. Hare and S. Yazdani, Quasi self-similarity and multifractal analysis of Cantor measures, Real Analysis Exch., 27 (2001/2), 287–307.
  • K. Hare and T. O’Neil, N-Fold Sums of Cantor sets, Mathematika, 47 (2000) 243–250.
  • C. Cabrelli, K. Hare and U. Molter, Sums of Cantor sets, Ergodic Theory and Dynamical systems 17 (1997), 1299–1313.

(c) Thin Sets

  • K. Hare and P. Mohanty, A non-abelian, non-Sidon completely bounded Lambda(p) set, accepted by Can. Math. Bull.
  • K. Hare and R. Yang, Sidon sets are proportionally Sidon with small Sidon constants, Can. Math. Bull. 62(2019), 798–809.
  • K. Hare and T. Ramsey, The ubiquity of Sidon sets that are not I0, Acta. Sci. Math. (Szeged) 82(2016), 509–518.
  • K. Hare and P. Mohanty, Completely bounded Lambda(p) sets that are not Sidon, Proc. Amer. Math. Soc., 144(2016), 2861–2869.
  • K. Hare and T. Ramsey, The relationship between e-Kronecker sets and Sidon sets, Can. Bull. Math. 59(2016), 521–527.
  • K. Hare and T. Ramsey, Exact Kronecker constants of three element sets, Acta Math. Hung. 146(2015), 306–331.
  • K. Hare and T. Ramsey, Kronecker constants of arithmetic progressions, Experimental Math. 23 (2014), 414–422.
  • K. Hare and S. Yamagishi, A generalization of Erd ̋os-Renyi to m-fold sums and differences, Acta Arith. 166 (2014), 55–67.
  • K. Hare and T. Ramsey, Exact Kronecker constants of Hadamard sets, Colloq. Math. 130 (2013), 39–49.
  • C. Graham and K. Hare, Existence of large ε-Kronecker sets and FFI0(U) sets in discrete abelian groups, Colloq. Math. 127 (2012), 1–15.
  • K. Hare and T. Ramsey, Kronecker constants for finite subsets of integers, J. Fourier Anal. and Applications 18 (2012), 326–366.
  • C. Graham and K. Hare, Characterizations of some classes of I0 sets, Rocky Mtn. J. 40 (2010), 513–525.
  • C. Graham and K. Hare, Sets of zero discrete harmonic density, Math. Proc. Camb. Phil. Soc. 148 (2010), 253–266.
  • D. Grow and K. Hare, Central interpolation sets for compact groups and hypergroups, Glasgow Math. J. 51 (2009), 593–603.
  • C. Graham, K. Hare and T. Ramsey, Union problems for I0 sets, Acta Sci. Math. (Szeged) 75 (2009), 175–195. Corrigendum, Acta Sci. Math. (Szeged) 76 (2010), 487–488.
  • C. Graham and K. Hare, I0 sets for compact, connected groups: Interpolation with measures that are non-negative or of small support, J. Aust. Math. Soc. 84 (2008), 199–215.
  • C. Graham and K. Hare, Characterizing Sidon sets by interpolation properties of subsets, Colloq. Math. 112 (2008), 175–199.
  • C. Graham and K. Hare, ε-Kronecker and I0 sets in abelian groups IV: Interpolation of non- negative measures, Studia Math., 177 (2006), 9–24.
  • C. Graham and K. Hare, ε-Kronecker and I0 sets in abelian groups I: Arithmetic properties of ε-Kronecker sets, Math. Proc. Camb. Phil. Soc., 140 (2006), 475–489.
  • C. Graham, K. Hare and T. Korner, ε-Kronecker sets and I0 sets in abelian groups II: Sparseness of products of ε-Kronecker sets, Math. Proc. Camb. Phil. Soc., 140 (2006), 491–508.
  • C. Graham and K. Hare, ε-Kronecker and I0 sets in abelian groups III: Interpolation of measures on small sets, Studia Math., 171 (2005), 15–32.
  • K. Hare and T. Ramsey, I0 sets in non-abelian groups, Math. Proc. Comb. Phil. Soc., 135 (2003), 81–98.
  • K. Hare, Random weighted Sidon sets, Colloq. Math., 86 (2000), 103–109.
  • K. Hare, Sidonicity in compact, abelian hypergroups, Colloq. Math. 96 (1998), 171–180.
  • K. Hare and D. Wilson, Weighted p-Sidon sets, J. Aust. Math. Soc. 61 (1996), 73–95.
  • K. Hare, Central Sidonicity for compact Lie groups, Ann. Inst. Fourier (Grenoble) 45 (1995), 547–564.
  • K. Hare, The support of a function with thin spectrum, Colloq. Math. 67 (1994), 147–154.
  • K. Hare and D. Wilson, Structural criterion for the existence of infinite central ∧(p) sets, Trans. Amer. Math. Soc. 337 (1993), 907–925.
  • K. Hare, Union results for thin sets, Glasgow Math. Journal 32 (1990), 241–254.
  • K. Hare, Strict-2-associatedness for thin sets, Colloq. Math. 56 (1988), 367–381.
  • K. Hare, Arithmetic properties of thin sets, Pac. J. Math. 131 (1988), 143–155.
  • K. Hare, An elementary proof of a result on ∧(p) sets, Proc. Amer. Math. Soc. 104 (1988), 829–834.

(d) Multipliers and Maximal Operators

  • A. Dooley, K. Hare and M. Roginskaya, On Lp-improving measures, Rev. Iberoamericana, 32(2016), 1211–1226.
  • K. Hare and M. Roginskaya, Directional maximal operators with smooth densities, Math. Nachr. 282 (2009), 1740–1752.
  • K. Hare and P. Mohanty, Distinctness of spaces of Lorentz-Zygmund multipliers, Studia Math., 169 (2005), 143-161.
  • K. Hare and F. Ricci, Maximal functions with polynomial densitites in lacunary directions, Trans. Amer. Math. Soc., 355 (2003), 1135–1144.
  • K. Hare and J-O. Ronning, Size of Max(p) sets and density bases, J. Fourier Anal. and Appl., 8 (2002), 259–268.
  • K. Hare and E. Sato, Spaces of Lorentz multipliers, Can. J. Math, 53 (2001), 565–591.
  • K. Hare, Maximal operators and Cantor sets, Can. Math. Bull., 43 (2000), 330–342.
  • K. Hare and J.-O. R ̈onning, Applications of generalized Perron trees to maximal functions and density bases, J. Fourier Anal. and App. 4 (1998), 215–227.
  • K. Hare, A general approach to Littlewood-Paley theorems for orthogonal families, Can. Math. Bull. 40 (1997), 296–308.
  • K. Hare and I. Klemes, On permutations of lacunary intervals, Trans. Amer. Math. Soc. 347 (1995), 4105–4127. (Featured Review in AMS Reviews 95m: 42027)
  • K. Hare and R. Grinnell, Lorentz-improving measures, Illinois J. Math. 38 (1994), 366–389.
  • K. Hare, Tame Lp-Multipliers, Colloq. Math. 64 (1993), 303–314.
  • K. Hare and I. Klemes, A new type of Littlewood-Paley partition, Arkiv for Mat. 30 (1992), 297–307.
  • K. Hare, The Size of (L2,Lp) multipliers, Colloq. Math. 63 (1992), 249–262.
  • K. Hare, Norm one multipliers, Can. Math. Bull. 35 (1992), 194–203.
  • K. Hare, Lp-Improving measures on compact non-abelian groups, J. Aust. Math. Soc. 46 (1989), 402–414.
  • C. Graham, K. Hare and D. Ritter, The size of Lp-improving measures, J. Func. Anal. 84 (1989) 472–495.
  • K. Hare and I. Klemes, Properties of Littlewood-Paley sets, Math. Proc. Camb. Phil. Soc. 105 (1989), 485–494.
  • K. Hare, Properties and examples of (Lp,Lq) multipliers, Indiana Univ. Math. Journal 38 (1989), 211–227.
  • K. Hare, A characterization of Lp-improving measures, Proc. Amer. Math. Soc. 102 (1988), 295–299.

(e) Miscellaneous Topics

  • S. Gupta and K. Hare, On convolution squares of singular measures, Colloq. Math., 100 (2004), 9–16.
  • K. Hare and A. Stokolos, On weak type inequalities for rare maximal functions, Colloq. Math., 83 (2000), 173–182.
  • K. Hare and J. Ward, Finite dimensional H-invariant spaces, Bull. Aust. Math. Soc. 56 (1997), 353–361.
  • K. Hare and M. Shirvani, The semisimplicity problem for p-adic group algebras, Proc. Amer. Math. Soc. 108 (1990), 653–664.

In refereed conference proceedings

  • K. Hare, Multifractal analysis of Cantor-like measures, New trends in applied harmonic analysis - sparse representations, compressed sensing and multifractal analysis. Ed. A. Aldroubi, C. Cabrelli, S. Jaffard and U. Molter, Birkhauser series of Applied and computational harmonic analysis, 350(2015), 1–19.
  • K. Hare and A. Stokolos, On the rate of tangential convergence of functions from Hardy spaces, 0 < p < 1, Contemporary Math. 370 (2005), 119–132.
  • K. Hare and N. Tomczak-Jaegerman, Banach space properties of translation invariant subspaces of Lp, Analysis at Urbana 1, London Math. Soc. Lecture Note Series 137, ed. E. Berkson, N. Peck & J. Uhl, Cambridge Univ. Press 1989, 185–195. 

Postdoctoral supervision

  • Sascha Troscheit, May 2017–Dec. 2018 (co-supervised with K.G. Hare)
  • Ignacio Garcia, Aug. 2015–Dec. 2016
  • Michael (Ka-Shing) Ng, January–April 2015
  • Leandro Zuberman, May 2009–April 2010
  • Denglin Zhou, January 2008–August 2009
  • Parasar Mohanty, September 2003–August 2004
  • Maria Roginskaya, September 2002–August 2003
  • Jan-Olav R ̈onning, September 1995–December 1995 and March 1996–June 1996

Graduate Supervision

PhD

  • Robert (Xu) Yang, “Sidon and Kronecker-like sets in compact abelian groups”, 2014–2019 (graduated)
  • Michael (Ka-Shing) Ng, “Some aspects of Cantor sets”, 2009–2014 (graduated)
  • Denglin Zhou, “Spectral analysis of Laplacians on certain fractals”, 2003–2007 (graduated)

MMath

  • Claudia Guerro, “Some applications of renewal theorem in fractal geometry”, 2019–2020 (graduated)
  • Samuel Desrochers, “Assouad dimension and non-embeddability”, 2019–2020 (graduated)
  • Robert (Xu) Yang, “Interpolation sets for compact Abelian groups”, 2013–2014 (graduated)
  • David Farahany, “Multiplier problem for the Ball and the Kakeya maximal operator”, 2012–2013 (graduated)
  • Sheena Tan, “Hadamard, ε-Kronecker and I0 sets in T”, 2010–2011 (graduated)
  • Vincent Chan, “On convolution squares of singular measures”, 2009–2010 (graduated)
  • Sheldon Stewart, “Construction of a Besicovitch Set”, 2008–2009 (graduated)
  • Pei Pei, “Hausdorff dimension of the random Cantor set”, 2008–2010 (graduated)
  • Keon Choi, “Maximal operators in R2”, 2005–2007 (graduated)
  • Karen Meagher, “Convolution estimates with Orlicz spaces”, 1995–1997 (graduated)
  • Hui Kong, “Riesz Product Measures”, 1991–1992 (graduated)