PUBLICATION LIST

[1] Harris, M.: Systematic growth of Mordell-Weil groups of abelian
varieties in towers of number fields. *Inventiones Math.***51**, 123-141 (1979).

[2] Harris, M.: A note on three lemmas
of Shimura. *Duke
Math. J.* **46**,
871-879 (1979).

[3] Harris, M.: P-adic representations
arising from descent on abelian varieties. *Compositio Math.* **39**, 177-245 (1979); Correction,
Compositio Math. (2000).

The principal error in this paper
was the incorrect claim that Iwasawa's sufficient criterion for a compact L-module to be torsion — that its group of
coinvariants be finite — generalizes to the non-abelian situation. A correct criterion,
involving the Euler characteristic, has since been found by Susan Howson.
Several proofs based on the fallacious criterion are replaced by alternative
proofs in the Correction. However, in the absence of a valid criterion,
it is impossible to justify the claim that certain modules constructed from
Selmer groups of elliptic curves are torsion L-module. Using the Euler characteristic criterion, Coates and Howson
found the first examples of torsion modules over the Iwasawa algebra of GL(2,**Z**_{p}) coming from Selmer groups of elliptic curves.

To my knowledge,the remainder of
the results of this paper are correct, when taken in conjunction with the
correction. This includes some of the basic structural theory of compact L-modules in the non-abelian case, the proof
that the L-module constructed from ideal class groups
(the direct analogue of the module studied by Iwasawa) is torsion, and certain
control theorems.

[4] Harris, M.: Kubert-Lang units and
elliptic curves without complex multiplication. *Compositio Math. ***41**, 127-136 (1980).

[RETRACTED]
Harris, M.: The annihilators of p-adic induced modules. *J. of Algebra*
**67**,
68-71 (1980). NOTE: Jordan Ellenberg has found a fatal flaw in the
main argument, so this paper should be disregarded. The problem is the
deduction on lines -2 and -3 of p. 69, which is
not justified. Ardakov and Wadsley have now shown (arXiv:1308.5104) that
the main result is false for every semisimple p-adic group.

[5] Harris, M.: The rationality of
holomorphic Eisenstein series. *Inventiones Math.* **63**, 305-310 (1981).

[6] Harris, M.: Special values of zeta
functions attached to Siegel modular forms. *Annales Scient. de l'Ec. Norm. Sup. ***14**, 77-120
(1981).

A rumor has been circulating to the
effect that one of the statements used in this article was not proved until
several years later, and that the proofs are
therefore incomplete. Apparently this is based on a misunderstanding. The
statement in question, as far as I can tell, is 3.6.2, the claim that the
antiholomorphic highest weight module for Sp(2n) is
irreducible down to weight n/2. This is of course a simple consequence of
the unitarity of the module (cited in 3.6.1), the fact that it is generatedby a
highest weight vector, and the well known fact that any submodule is generated
by highest weight vectors. If there is anything more to the rumor I
don't know what it is.

[7] Harris, M.: Maass operators and
Eisenstein series. *Math. Ann. ***258**, 135-144 (1981).

[8] Harris, M.: P-adic measures for
spherical representations of reductive p-adic groups. *Duke Math. J. ***49**, 497-512 (1982).

[9] Harris, M., Jakobsen, H.P.:
Singular holomorphic representations and singular modular forms. *Math. Ann.* **259**,
227-244 (1982).

[10] Harris, M., Jakobsen, H.P.:
Covariant differential operators, in Group Theoretical Methods in Physics
(Istanbul, 1982), *Lecture Notes in Physics*, **180**, 16-34. Berlin:
Springer-Verlag (1983).

[11] Harris, M.: Eisenstein series on
Shimura varieties. *Ann. of Math.* **119**, 59-94 (1984).

[12] Harris, M.: Arithmetic vector
bundles on Shimura varieties, in Automorphic Forms of Several Variables,
Proceedings of the Taniguchi Symposium, Katata, 1983 , 138-159. Boston:
Birkhaüser (1984).

The argument in 3.5 of this mainly
expository paper, concerning jet bundles, is nonsense. A correct argument
is given in the subsequent articles.

[13] Harris, M.: Arithmetic vector
bundles and automorphic forms on Shimura varieties. I. *Inventiones Math.* **82**, 151-189 (1985).

The term "arithmetic vector
bundle" has since been replaced by "automorphic vector
bundle". The argument in (3.6.7), deriving existence of a model over a number field of an "absolutely
arithmetic" automorphic vector bundle by means of a cocycle condition
involving Aut(**C**),
needs further justification. [SEE NOTE BELOW.] A simpler alternative is to
observe that a quotient of the canonical principal bundle I(G,X) by a finite
subgroup C of the center of G is already
defined over the reflex field E(G,X). One can take C to be the
intersection of the center of G with the derived subgroup G^{der}.
Indeed, the fact that the quotient of I(G,X) by the center of G is defined over
E(G,X) follows from Proposition 3.7, whereas the fact that the quotient by G^{der}
is defined over E(G,X) is a conseqence of the theory for tori. Since
finite étale covers are defined over finite algebraic extensions, one sees
immediately that I(G,X) is defined over some number field, as are the Hecke
correspondences on I(G,X). One can then replace the cocycle

for Aut(**C**) by a continuous cocycle on the Galois group
of the algebraic closure of **Q**. A complete argument may be given elsewhere.

NOTE ADDED MARCH 21, 2008:
After rereading Shimura's original proof of the existence of canonical models

using cocycles on Aut(**C**) [Shimura, *Annals of Math.***, 83 **(1966) 294-338] in the light of its reformulation by

Varshavsky [Appendix to *Selecta Math.*, **8 **(2002) 283-314], I am now convinced that the argument in (3.6.7)
is essentially correct.

The argument proceeds by constructing a cocycle on Aut(**C**) with values in **G**m that is shown to be effective for
descending to

an appropriate reflex field an automorphic vector bundle on the Shimura variety
attached to a torus. It thus necessarily

satisfies the required continuity property. All that is missing from the
proof is acknowledgment of of this requirement.

[14] Harris, M.: Arithmetic vector
bundles and automorphic forms on Shimura varieties II. *Compositio Math*. **60**, 323-378 (1986).

[15] Harris, M., Phong, D. H.:
Cohomologie de Dolbeault à croissance logarithmique à l'infini. *C. R. Acad. Sci.
Paris***
302**, 307-310 (1986).

José Ignacio Burgos pointed
out in 1997 that the argument in Griffiths-Harris, used to extend the Poincaré
Lemma with logarithmic singularities from the one-dimensional case to the
general case, does not apply in the present situation. Briefly, the
Dolbeault complex defined in this paper consists of forms w which, together with their antiholomorphic
derivatives, satisfy logarithmic growth conditions in the neighborhood of a
divisor with normal crossings. However, the Griffiths-Harris argument
introduces additional holomorphic derivatives, which may not belong to the
original complex. The quotation
should have been of the argument used by Borel in reference [1], which is based
on integration rather than differentiation.

As noted in [19], and as observed
independently by Burgos, one can actually reprove the one-dimensional Poincaré
lemma with logarithmic singularities for forms all of whose derivatives,
holomorphic as well as anti-holomorphic, satisfy the growth conditions; this is
even necessary if one wants to obtain Lie algebra cohomology complexes to
calculate the cohomology of Shimura varieties. A complete proof of this
fact, and the correct deduction of the higher-dimensional case, was published
in [42], in response to Burgos' comment.

[16] Harris, M.: Formes automorphes
"géométriques" non-holomorphes: Problèmes d'arithméticité, in *Sém de Théorie
des Nombres, Paris 1984-85* Boston: Birkhaüser (1986).

[17] Harris, M.: Arithmetic
of the oscillator representation, manuscript (1987), see this page.

[18] Harris, M.: Functorial properties
of toroidal compactifications of locally symmetric varieties, *Proc. Lon. Math.
Soc.* **59**,
1-22 (1989)

[19] Harris, M.: Automorphic forms and
the cohomology of vector bundles on Shimura varieties, in L. Clozel and J.S.
Milne, eds., *Proceedings
of the Conference on Automorphic Forms, Shimura Varieties, and L-functions, Ann
Arbor, 1988*, *Perspectives
in Mathematics*, New York: Academic Press, Vol. II, 41-91
(1989).

[20] Harris, M.: Automorphic forms
of d-bar-cohomology type as coherent cohomology classes, *J. Diff. Geom.*
**32**, 1-63
(1990).

[21] Harris, M.: Period invariants of
Hilbert modular forms, I: Trilinear differential operators and
L-functions, in J.-P. Labesse and J. Schwermer, eds., Cohomology of Arithmetic
Groups and Automorphic Forms, Luminy, 1989, *Lecture Notes in Math.*, **1447**, 155-202 (1990).

The last section of this article
assumes the extension of the techniques of [22] to general totally real
fields. At the time of publication, I was under the mistaken impression that
the Siegel-Weil formula for the central value of the Eisenstein series, proved
by Kudla and Rallis, extended in a simple way to the symplectic similitude
group GSp(6). In fact, the extension proposed in [22] only works over **Q**. A
correct Siegel-Weil formula for similitude groups is proved in [49]. Thus
the proofs in this article are now complete.

[22] Harris, M., Kudla, S.: The central
critical value of a triple product L-function, *Ann. of Math*., **133**, 605-672 (1991).

[23] Harris, M., Kudla, S.: Arithmetic
automorphic forms for the non-holomorphic discrete series of GSp(2), *Duke Math. J. ***66**, 59-121
(1992).

[24] Garrett, P.B., Harris, M.: Special
values of triple product L-functions, *Am. J. Math.* **115**, 159-238 (1993).

[25] Harris, M.: Non-vanishing
of L-functions of 2x2 unitary groups, *Forum Math.* **5**, 405-419 (1993).

[26] Harris, M., Soudry, D., Taylor,
R.: l-adic representations attached to modular forms over an imaginary
quadratic field, I: lifting to GSp(4,**Q**), *Inventiones Math.*, **112**, 377-411 (1993).

On p. 410, lines 2-3, we claim to
have constructed supercuspidal representations of GSp(4) over a p-adic field
that were missed by Vignéras in her article [V]. Dipendra Prasad pointed
out that these supercuspidal representations, and the corresponding
representations of the Weil group, were actually constructed in [V] in a
different matrix representation.

[27] Harris, M.: L-functions of 2 by 2
unitary groups and factorization of periods of Hilbert modular forms, *J. Am. Math. Soc.*
**6**,
637-719, (1993).

The relation of CM periods to
special values of L-functions of Hecke characters, obtained in general by
Blasius, is quoted on numerous occasions in this article. Unfortunately,
it is quoted here, as in the appendix to [22], with a sign mistake. The
final formulas are indifferent to the choice of sign, so no harm is done.
The mistake is corrected in the introduction to [35], whose results depend on
the correct choice of sign.

[28] Harris, M., Zucker, S.: Boundary
cohomology of Shimura varieties, I: coherent cohomology on the
toroidal boundary, *Annales Scient. de l'Ec. Norm. Sup.* **27**, 249-344 (1994).

[29] Harris, M., Zucker, S.: Boundary
cohomology of Shimura varieties, II: mixed Hodge structures , *Inventiones Math.***116**, 243-307
(1994); Erratum, *Inventiones
Math.*, **123**, 437 (1995).

[30] Harris, M.: Hodge-de Rham
structures and periods of automorphic forms, in Motives, *Proc. Symp. Pure Math.. AMS*, **55**, Part 2,
pp. 573-624 (1994).

[31] Blasius, D., Harris, M.,
Ramakrishnan, D.: Coherent cohomology, limits of discrete series, and
Galois conjugation, *Duke Math. J, * **73**, 647-686 (1994).

[32] Harris, M.: Period invariants of
Hilbert modular forms, II, *Compositio Math. ***94**, 201-226 (1994).

[33] Harris, M., Kudla, S., Sweet, W.
J.: Theta dichotomy for unitary groups, *J. Am. Math. Soc.***9**, 941-1004 (1996).

[34] Harris, M.: Supercuspidal
representations in the cohomology of Drinfel'd upper half spaces; elaboration
of Carayol's program, *Inventiones Math.* **129**, 75-119 (1997).

The correction character,
denoted n(Gp) on p. 100, is calculated incorrectly on
p. 101. The correct calculation is given on p. 181 of [37], where the sign convention of
[34] is also replaced by one consistent with the conventions of the book of
Rapoport and Zink.

[35] Harris, M.: L-functions and
periods of polarized regular motives, *J.Reine Angew. Math.***483**, 75-161 (1997).

The main result on special
values of L-functions of automorphic forms on unitary Shimura varieties refers
to an unpublished calculation of archimedean zeta integrals, due to P.
Garrett (Lemma 3.5.3). Garrett has since written up this calculation in a
more general setting and his results are included in the same volume as [53].

[36] Harris, M. , Li, J.-S.: A
Lefschetz property for subvarieties of Shimura varieties, *J. Alg. Geom. ***7**, 77-122 (1998).

[37] Harris, M.: The local
Langlands conjecture for GL(n) of a p-adic field, n < p, *Inventiones Math.*
**134**,
177-210 (1998).

[38] Harris, M.: Cohomological automorphic
forms on unitary groups, I: rationality of the theta correspondence, *Proc. Symp. Pure
Math,* **66.2**,
103-200 (1999).

A great many misprints were
discovered while preparing the sequel [55]. There were also a few
substantial mathematical errors. These were all corrected in the
introduction to [55].

[39] Harris, M.: Galois properties of
cohomological automorphic forms on GL(n), *J. Math. Kyoto Univ. ***39**, 299-318 (1999).

[40] Harris, M., Tilouine, J.: p-adic
measures and square roots of triple product L-functions, *Math. Ann.*, **320**,
127-147 (2001).

A recent article by Darmon and
Rotger has found a different formula for the corrected Euler factor at p in
Proposition 2.2.2. There must be an error in our (elementary)
calculation, but we have not yet been able to find it.

[41] Harris, M., Scholl, A.: A note on
trilinear forms for reducible representations and Beilinson's conjectures, *J. European Math.
Soc.*, **3**,
93-104 (2001).

[42] Harris, M., Zucker, S.: Boundary
cohomology of Shimura varieties, III: Coherent cohomology on higher-rank
boundary strata and applications to Hodge theory, *Mémoires de la SMF,* **85** (2001).

[43] Harris, M., Taylor, R.: The
geometry and cohomology of some simple Shimura varieties, *Annals of
Mathematics Studies*, **151** (2001).

[44] Harris, M.:
Local Langlands correspondences and vanishing cycles on Shimura varieties,
Proceedings of the European Congress of Mathematics, Barcelona, 2000; *Progress in
Mathematics*, **201**, Basel: Birkhaüser Verlag, 407-427 (2001).

Eva Viehmann has found a mistake in
the statement of Proposition 4.1 (ii), which means that Conjecture 5.2 needs to
be corrected. The statements seem to be all right for split groups
but not in the general case. Viehmann has proposed a corrected version.
See item [51] below.

[45] Harris, M., Taylor, R.: Regular models of certain Shimura varieties,
*Asian J. Math.***6**, 61-94
(2002).

[46] Harris, M.: On the local
Langlands correspondence, in Proceedings of the International Congress of
Mathematicians, Beijing 2002, Vol II, 583-597.

[47] Harris, M., Taylor, R.:
Deformations of automorphic Galois representations (manuscript, 1998-2003).

[48] Harris, M., Kudla, S.: On a
conjecture of Jacquet, in H. Hida, D. Ramakrishnan, F. Shahidi, eds.,
Contributions to automorphic forms, geometry, and number theory (collection in
honor of J. Shalika's 60th birthday), 355-371 (2004).

[49] Harris, M.:
Occult period invariants and critical values of the degree four L-function of
GSp(4) in H. Hida, D. Ramakrishnan, F. Shahidi, eds.,

Contributions to automorphic forms, geometry, and number theory (collection in
honor of J. Shalika's 60th birthday), 331-354 (2004).

[50] Harris, M., Labesse, J-P.: Conditional base change for
unitary groups, *Asian
J. Math*, **8**, 653-684 (2004).

[51] Harris, M.: The Local Langlands correspondence: Notes of
(half) a course at the IHP, Spring 2000, in J. Tilouine, H. Carayol, M.
Harris, M.-F. Vignéras, eds., Formes Automorphes, *Astérisque*, **298**, 17-145 (2005) .

The mistake in [44] arises from an
incorrect argument on pp. 130-131 of this article. Viehmann has published
a corrected version in a joint
paper with Rapoport. I hope to
revise the calculation of the global Galois representation as a sum of
contributions of individual strata.

[52] Harris, M., Li, J.-S., et Skinner, C.: The Rallis inner
product formula and p-adic L-functions, in J. Cogdell et al., eds, Automorphic
Representations, L-functions and Applications: Progress and Prospects,
Berlin: de Gruyter, 225-255 (2005).

[53] Harris, M. : A simple proof of rationality of Siegel-Weil
Eisenstein series, in W.T. Gan, S.S. Kudla, and Y. Tschinkel, eds.,

*Eisenstein
Series and Applications*, Boston: Birkhäuser, *Progress in
Mathematics* **258 **(2008) 149-186 (preceded by appendix by P. Garrett).

[54] Harris, M., Li, J.-S., et Skinner, C.: p-adic L
functions for unitary Shimura varieties, I : Construction of the
Eisenstein measure, *Documenta Math.*, ** **John H. Coates' Sixtieth Birthday 393-464
(2006).

[55] Harris, M.: Cohomological automorphic forms on unitary
groups, II: period relations and values of L- functions in Li, Tan,
Wallach, and Zhu, eds., Harmonic Analysis, Group Representations, Automorphic
Forms and Invariant Theory, Vol. 12, Lecture Notes Series, Institute of
Mathematical Sciences, National University of Singapore (volume in honor of
Roger Howe) (2007) 89-150.

[56] Clozel, L., Harris, M., and Taylor, R. : Automorphy for some
l-adic lifts of automorphic mod l Galois representationsm *Publ. Math. IHES*,
**108**
1-181 (2008).

[57] Harris, M., Shepherd-Barron, N, and Taylor, R.: A family of
Calabi-Yau varieties and potential automorphy, *Annals of Math.*, **171**, 779-813 (2010).

[58] Harris, M., Potential automorphy of odd-dimensional symmetric powers
of elliptic curves, and applications in *Algebra, Arithmetic, and Geometry: In Honor of Yu.
I. Manin*, Vol II,
Boston: Birkhäuser, *Progress in Mathematics*, **270** (2009) 1-23.

[59] Harris, M.: Arithmetic applications of the Langlands program, *Japanese J. Math.*,
3rd ser., **5**
(2010) 1-71.

[60] Guralnick, R., Harris, M., Katz, N. : Automorphic realization
of Galois representations, *J. Euro. Math. Soc.*, **12**, (2010) 915–937.

[61] Harris, M. : An introduction to the stable trace formula, in L.
Clozel, M. Harris, J.-P. Labesse, B. C. Ngô, eds. *The stable trace formula, Shimura varieties,
and arithmetic applications. Volume I: Stabilization of the trace formula*,
Boston: International Press (2011) 3-47.

[62] Clozel, L., Harris, M., Labesse, J.-P.: Endoscopic
transfer, in L. Clozel, M. Harris, J.-P. Labesse, B. C. Ngô, eds. *The stable trace
formula, Shimura varieties, and arithmetic applications. Volume I:
Stabilization of the trace formula*, Boston: International Press
(2011) 475-496.

[63] Clozel, L., Harris, M., Labesse, J.-P.: Construction of automorphic
Galois representations, I., in L. Clozel, M. Harris, J.-P. Labesse, B. C. Ngô,
eds. *The
stable trace formula, Shimura varieties, and arithmetic applications. Volume
I: Stabilization of the trace formula*, Boston: International
Press (2011) 497-527.

[64] Harris, M., Li, J.-S.. Sun, Binyong, Theta correspondence for close
unitary groups, *Advanced
Lectures in Mathematics*, special issue in honor of S. Kudla, (2011)
265-308.

[65] Barnet-Lamb, T., Geraghty, D., Harris, M., et Taylor, R. : A
family of Calabi-Yau varieties and potential automorphy II, *Proceedings RIMS*,
**47**
(2011) 29-98.

[66] Chenevier, G.,
Harris, M., Construction of automorphic Galois representations, II, ** Cambridge Journal of Mathematics**,

[67] Harris, M. : The Taylor-Wiles method for coherent
cohomology, *J.
Reine Angew. Math.*, **679** (2013) 125-153.

[68]
Harris, M.: L-functions and periods of adjoint motives, *Algebra and Number Theory*, **7** (2013), 117-155.

[69] Harris, M.: Beilinson-Bernstein
localization over **Q** and periods of automorphic forms,

** International Math. Research Notices**,

Fabian Januszewski
has pointed out a group of related errors in this article, as well as an
ambiguity and a few arguments based on constructions for which there are not
references in the literature. The
main point is that some of the modules only have models over finite extensions
of their fields of coefficients.
This has no bearing on applications to special values of L-functions,
but the statements have to be corrected.
An erratum is in preparation.

[70] Harris, M.:
Weight zero Eisenstein cohomology of Shimura varieties via Berkovich
spaces, *Pacific
J. Math.* (supplement to special issue in memory of J. Rogawski), **268 ** (2014), 275–281.

[71] Harris, M.:
Testing rationality of coherent cohomology of Shimura varieties, in J.
Cogdell *et
al.,* eds, *Automorphic
Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro*,
*Contemporary
Mathematics*, **614** (2014) 81-95.

[72] Harris, M. : Galois
representations, automorphic forms, and the Sato-Tate conjecture, *Indian
Journal of Pure and Applied Mathematics*, **45**, (2014) 707-746.

[73] Harris, M.:
Automorphic Galois representations and the cohomology of Shimura
varieties, in *Proceedings
of the International Congress of Mathematicians*, Seoul 2014.

[74] Grobner, H., Harris, M.:
Whittaker periods, motivic periods, and special values of tensor product
L-functions, *Journal
of the Institut de Mathématiques de Jussieu*, **15** (2016) 711-769.

[75] Grobner, H., Harris, M., Lapid, E.: Whittaker regulators and non-critical values of Asai
L-functions, *Contemporary
Mathematics*, **664** (2016) 119-134.

[76] Harris, M., Lan, K-W., Taylor, R., and Thorne, J., On the
rigid cohomology of certain Shimura varieties, *Research in the Mathematical Sciences*,
Special Collection in honor of Robert Coleman, **3**: 39, (2016)

[77] Harris, M.: p-adic and analytic properties of period integrals
and values of L-functions, *Annales des Mathématiques du Québec*, **40**(2) (2016) 435-452, special issue in
honor of G. Stevens.

[78] Harris, M.:
Speculations on the mod p representation theory of p-adic groups, *Annales de la
Faculté des sciences de Toulouse*, **25**, (2016) 403-418, special issue in honor of V. Schechtman.

[79] Harris, M., Lin, J.:
Period relations and special values of Rankin-Selberg L-functions, to
appear in *Contemporary
Math.*, special issue in honor of Roger Howe (2016).

[80] Eischen, E., Harris, M.,
Li, J.-S., Skinner, C.:
p-adic L functions for unitary Shimura varieties, II : zeta integral calculations;
III : ordinary families and
p-adic L-functions, arXiv: 1602.01776
[math.NT].

[81] Böckle, G., Harris, M., Khare, C., Thorne, J.: G^-local systems on smooth projective curves are
potentially automorphic, arXiv:1609.03491
[math.NT].

[82] Esnault,
H., Harris, M.: Chern classes of
automorphic vector bundles, arXiv:
1701.09073 [math.AG]

**Other publications**

1. Review of Holomorphic Hilbert
Modular Forms (P. Garrett), *Bull. AMS*, **25**, 184-195 (1991)

2. Contexts of Justification, *Math.
Intelligencer*, Winter 2001.

3. Review of *Cohomologie,
stabilisation, et changement de base* (J.-P. Labesse), *Gazette des
Mathématiciens,* 2001.

4. Review of *Mathematics and the Roots of Postmodern
Thought *(V. Tasic), *Notices of the AMS*, August 2003 .

5. Review of
Introduction to the Langlands Program (J. Bernstein et S. Gelbart), *Bull. AMS*
**41**
257-266 (2004).

6. A sometimes funny book supposedly about infinity, review of *Everything and
More* (D.F. Wallace), *Notices of the AMS*, **51**, 632-638, June-July 2004.

7. “Why mathematics?” you might ask, in T. Gowers, ed. *The Princeton
Companion to Mathematics*, Princeton University Press (2008) 966-977.

8. Unexpected,
Economical, Inevitable*, Tin House*, **50 **(2011).

9. Do Androids Prove Theorems in
Their Sleep?, in A. Doxiadis and B. Mazur, eds, *Circles Disturbed*, Princeton University
Press (2012).

10. Sudden
disorientation in a Paris museum, *Notices of the AMS*, **59**, 822-826, June-July 2012.

11.
Dispatch from the Oscars of
Science, www.slate.com, November 19, 2014.

12. *Mathematics
without Apologies: A Portrait of a
Problematic Vocation*, Princeton University Press, January 2015.

13. Mathematicians
of the future? www.slate.com,
March 23, 2015

14. Review
of *How Not to
Be Wrong* (J. Ellenberg), *Nature*, *Books & Arts Special*, July 2015.

15. The mercurial mathematician, Review of *Genius at Play*
(S. Roberts), *Nature*, **523**, July 23, 2015, 406-7.

16. Review of *Birth of a
Theorem* (C. Villani), *American Mathematical Monthly*, **122** (2015) 1018-1022.

17. The perfectoid
concept: test case for an absent
theory, to appear in Coles, deFreitas, and Sinclair, eds. *What is a Mathematical Concept?* Cambridge: Cambridge University Press.

18. Visions of That
Which is Sought*,*
to appear in *Social
Research: an International
Quarterly*, special issue on "Invisibility," **83:4 **(Winter 2016).