Harvard Mathematics Department : Graduate Information

Admissions

To request application forms for admission and financial aid and additional information on the Ph.D. program in mathematics, please go to the web site http://www.gsas.harvard.edu or write to the with all other requests, please write to the Graduate Studies Coordinator of the Mathematics department. Here are the addresses and links:

Admissions Office of the
Graduate School of Arts and Sciences
Harvard University
Holyoke Center 350
1350 Massachusetts Avenue
Cambridge, MA 02138-3846
Phone: (617) 495-5396
Fax: (617) 496-5333

GSAS Links:

Mathematics Department
Graduate Studies Coordinator:
Irene Minder
(617) 495-2170
irene@math

All graduate students are admitted to begin their studies in the fall semester. We plan on an entering class of about ten to twelve students. Since we normally get over two hundred applications, the competition is keen. Financial aid in the form of scholarships and/or Teaching Fellowships is available. In general students without outside support will get scholarship support in their first year, but are required to act as a teaching fellow for one half course (i.e. for a one semester course) in their second through fourth years and for two half courses if they stay for a fifth year.

Applicants are encouraged to seek out and apply for sources of financing graduate study such as NSF Graduate Fellowships, Hertz Graduate Fellowships, NDSEG Fellowships. Applicants from the UK are urged to also apply for the Kennedy fellowships and applicants from UK, New Zealand, Canada and Australia, for Knox fellowships.

We do not grant a terminal Master's, but a Master's degree can be obtained "on the way" to the Ph.D. by fulfilling certain course and language exam requirements.

In general, there isn't a "transfer" status of application to the Graduate School of Arts and Sciences, nor to the Department of Mathematics. There is no formal "credit" given for an M.Sc. or M.A. and you would be considered as a first-year applicant along with all others applying. Once you arrive, the only difference that your degree will make is that you might be in a better position to prepare for our Qualifying Exam, which is required of all students.

The Division of Engineering and Applied Sciences offers both a Master's Degree program and a Ph.D. program in Applied Mathematics. The Dean of this Department is Professor Venkatesh Narayanamurti. Information is available from

Division of Engineering and Applied Sciences
212a Pierce Hall
29 Oxford St.
Cambridge, MA 02138
URL: http://www.deas.harvard.edu

A list of courses at the Mathematics department can be found here.

Guide To Graduate Study

The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students to develop their understanding and enjoyment of mathematics. It seems to be generally the case that enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in one's own way. For this reason, a thesis involving some original research is a fundamental part of the program. The stages in this program may be described as follows:

Acquiring a broad basic knowledge of mathematics on which to build a future mathematical culture and more detailed knowledge of a field of specialization.
Choosing a field of specialization within mathematics and obtaining enough knowledge of this specialized field to arrive at the point of current thinking.
Making a first original contribution to mathematics within this chosen special area.

The word "help" (in the opening sentence above) is to emphasize that the student is expected to take the initiative in pacing him or herself through the Ph.D. program. In theory, a future research mathematician should be able to go through all three stages with the help of only a good library. In practice, many of the more subtle aspects of mathematics, such as a sense of taste or relative importance and feeling for a particular subject, are primarily communicated by personal contact. In addition, it is not at all trivial to find one's way through the ever-burgeoning literature of mathematics, and one can go through the stages outlined above with much less lost motion if one has some access to a group of older and more experienced mathematicians who can guide one's reading, supplement it with seminars and courses, and evaluate one's first attempts at research. The presence of other students of comparable ability and level of enthusiasm is also very helpful.

The University requires a minimum of two years academic residence for the Ph.D. degree. On the other hand, five years in residence is the maximum usually allowed by the Department of Mathematics. Many students finish in four years. This is strongly encouraged. A fifth year is allowed if during the fourth year there is some positive progress towards a thesis, giving the advisor confidence that the student has a good chance of completing the thesis within a year. If a student has not completed her or his dissertation while here, she or he can finish it elsewhere and submit it at a later date.

There are no specific course requirements. Students must register for four courses each semester, except that they may substitute time (i.e. independent study) for one of these courses (or for two if they are teaching). Once the qualifying exam has been passed students are automatically Excused from getting a grade in any math course.

The department runs several introductory graduate courses (e.g. math 212a, 213a, 230a, 250a, 260ab, 272ab) to help students acquire the necessary broad basic background in mathematics. The department also gives a biannual qualifying examination (usually in September and February) to help students assess their progress. One's first goal should be to bring one's basic knowledge up to such a point that one can pass the qualifying exam. Before passing it students are required to take courses for credit (usually 3 or 4 a semester). After passing it they simply get an EXCused grade for any math course they may take. Some students are able to pass as soon as they enter and all are urged to try as soon as they think that there is any chance of passing. Those who fail simply try again on the following occasion. Even for those who are not yet fully prepared the qualifying exam can provide a useful diagnostic. All students should pass the qualifying exam before the end of their second year.

The qualifying examination covers algebra, algebraic geometry, algebraic topology, complex analysis, differential geometry, and real analysis. It usually consists of three, three hour papers on three consecutive days. Each paper typically has 6 questions. To pass one must score about 120 out of a possible 180. There are Conditional passes as well for those who show a weakness in just one or two areas. These count for EXCused status in general, but require the student to take a specific course for a grade at the next opportunity. More details about the qualifying exams can be found here.

After passing the qualifying examination there are three other requirements for students besides the thesis.

The minor thesis is in some sense complementary to the qualifying exam. As it is set up, passing the qualifying exam does not mean that there are no gaps in the student's knowledge, only that s/he has enough background to commence work on his/her own. In the course of this work the student will inevitably encounter areas in which s/he is ignorant. The minor thesis is an exercise in filling such a gap: the student takes an unfamiliar subject and, within a finite time (three weeks, or four if teaching), learns it well enough to give a coherent exposition of it. The topic is selected by the student in consultation with a supervising faculty member of the student's choice. At the end of the allowed time, the student will submit to the supervising faculty member an oral presentation and a written account of the subject. The minor thesis must be completed before the start of the student's fifth semester in residence.

Mathematics is an international subject in which the principal languages are English, French, German, and Russian. Almost all important work is published in one of these four languages, although much Russian work is translated into English. Accordingly, every student is advised to acquire an ability to read mathematics in French, German, and Russian, as soon as possible, and is required to demonstrate it by passing a two-hour, written examination in each of two of these three languages. (Usually students are asked to translate about one page of mathematics into English with the help of a dictionary if needed. A student who thinks it is pertinent to his/her field of interest may substitute Italian for one of the languages mentioned above.) The first language requirement should be fulfilled by the end of the second year; the second language exam passed by the end of the third year.

Most research mathematicians are also university teachers. In preparation for this role all our students are required to take a teaching apprenticeship and to have two semesters of classroom teaching experience, usually as a Teaching Fellow. During the teaching apprenticeship the student is paired with a member of our teaching staff. The student will attend some of the adviser's classes and then prepare (with help) and present his/her own class, which will be videotaped. There will be feedback from the adviser and from members of the class. Teaching Fellows are responsible for teaching calculus to a class of about 25 undergraduates. They meet with their class 3 hours a week. They have a course assistant (usually an advanced undergraduate) to grade homework and to take a weekly problem session. Usually there are several classes following the same syllabus and with common exams. There is a course head (a member of our teaching staff) who will coordinate the various classes following the same syllabus and who is available to advise Teaching Fellows. Sometimes graduate students also act as graduate course assistants for advanced courses or run tutorials for small groups of undergraduates studying subjects not taught in our regular courses.

Upon completion of one language exam and having taken 8 "real" courses (not "time"), one can apply for a Master's Degree. This may be useful for higher paying summer jobs (and as another line on your resume). It also entitles one to attend and receive tickets for commencement. There is no fee.

How a student goes through the second and third stages varies considerably among individuals. While preparing for the qualifying examination or immediately after, the student should be taking or auditing more advanced courses and trying to decide upon a field of specialization. Unless prepared to work independently, she or he should choose a field which falls within the interests of some member of the faculty who is willing to serve as thesis advisor. Members of the faculty vary a great deal in the way that they go about thesis supervision and the student should take her or his own needs in this direction into account as well as the faculty member's field in making a decision. Some faculty members expect more initiative and independence than others, and they also vary in how busy they are with other students. In the event that no member of the Department suits a particular student, there is also a possibility of asking an M.I.T. professor for guidance. In any case, the student must take the initiative and ask a professor if she or he will act as thesis advisor. If one has trouble in deciding under whom to work, it is possible to spend a semester reading under the direction of two or more faculty members simultaneously on a tentative basis. The sooner a decision is made the better, and if at all possible it should be done during the second year.

It is important to keep in mind that no technique has been or ever will be discovered for teaching students to have ideas. All that the faculty can do is to provide an ambience in which one's nascent abilities and insights can blossom. Moreover, Ph.D. theses vary enormously in quality, from hard exercises to highly original advances. Finally, many very good research mathematicians begin very slowly, and their theses and first few papers could be of minor interest. On the whole, we feel that the ideal attitude is: (1) a love of the subject for its own sake, accompanied by inquisitiveness about things which aren't known; and (2) a somewhat fatalistic attitude concerning "creative ability", and recognition that hard work is, in the end, much more important.

The Qualifying Exam

The qualifying exam in mathematics is designed to measure the breadth of a student's knowledge in mathematics. The exam may identify those areas in which a student's knowledge is weak. Passing the exam is an indication that a student is ready to begin more specialized study leading to research work.

The exam is given at the very start of each semester. A student may take the exam as often as (s)he likes. There is absolutely no stigma attached to `failing' the exam. `Failing' it may well provide more useful information than `passing' it. `Passing' the exam early is mainly an indication that a student has been an undergraduate at a university with a broad undergraduate program in mathematics. It is not a good predictor of the quality of the eventual PhD thesis.

Students are strongly encouraged to first take the exam no later than their second semester. Before passing the qualifying exam, students should take three beginning 200 level (or 100 level) math courses each semester. In a semester in which they are teaching they need only take two such courses. After passing the qualifying exam students are usually excused from grades in any math courses they take. Students are expected to pass the qualifying exam by the end of their second year.

The exam consists of three three hour papers on three consecutive days. Each paper typically has 6 questions covering a broad range of mathematics. The questions aim to test your ability to solve concrete problems by identifying and applying important theorems. They should not require great ingenuity. In any given year the exam may not cover every topic on the syllabus, but it should cover a broadly representative set of quals/topics and over time all quals/topics should be examined.

The Qualifying Exam Syllabus

The syllabus is divided into 6 areas. In each case we suggest (sections of) a book to more carefully define the syllabus. The examiners are asked to limit their questions to major quals/topics covered in (these sections of) these books. We have tried to choose books we think are good. However there are many good books and others might better suit your needs. In each case we divide the syllabus into two sections. Section U is material which are usually covered in our undergraduate, not our graduate, courses. Section G is material usually taught at the graduate level. Where appropriate we list courses which will cover some of this material.

1) Algebra. U: Dummit+Foote, Abstract Algebra, except chapters 16 and 17. (math 122, 123) G: Dummit+Foote, Abstract Algebra, chapter 17.	2) Algebraic Geometry G: Harris, Algebraic geometry, a first course, lectures 1-7, 11, 13,14, 18. (math 137 and math 232a)	3) Complex Analysis (Table of contents) U: Ahlfors, Complex Analysis (2nd ed), chapters 1-4 and section 5.1. (math 113) G: Ahlfors, Complex Analysis (2nd ed), section 5.4.
4) Algebraic Topology U: Hatcher, Algebraic Topology, chapter 1 (but not the additional quals/topics). (math 131) G: Hatcher, Algebraic Topology, chapter 2 (including additional quals/topics) and chapter 3 (without additional quals/topics). (math 231a)	5) Differential Geometry (Table of contents) U: Boothby, An introduction to differentiable manifolds and Riemannian geometry, sections VII.1 , VIII.1 and VIII.2. (math 136) G: Boothby, An introduction to differentiable manifolds and Riemannian geometry, chapters I - V and VII. (math 132 and 230a)	6) Real Analysis (Rudin: Table of contents) (Birkhoff+Rota: Table of contents) U: Rudin, Principles of mathematical analysis, chapters 1-8. Birkhoff + Rota, Ordinary differential equations, chapters 1-4 and 6. (math 25, 55, 112) G: Rudin, Principles of mathematical analysis, chapter 10. G: Rudin, Functional analysis, chapters 1, 2, 3.1-3.14, 4, 6, 7.1-7.19 and 12.1-12.15. (math 212a)

Some Old Qualifying Exams

Some old departmental qualifying exams are available here:

(Fall 1995 pdf)	(Fall 2001 pdf)	(Fall 2002 pdf)	(Fall 2003 pdf)	(Fall 2004 pdf)	(Fall 2005 pdf)	(Fall 2006 pdf)
(Spring 1996 pdf)	(Spring 1997 pdf)	(Spring 2003 pdf)	(Spring 2004 pdf)	(Spring 2005 pdf)	(Spring 2006 pdf)	(Spring 2007 pdf)	(Spring 2008 pdf)

Some PDF files of questions arranged by topics.

Collected by Danny Calegari and Tom Coates source.

Teaching Requirements

For those students without outside support: In your first year we automatically offer you the full departmental stipend and you have no obligation to teach. In your second, third and fourth years we offer you half the departmental stipend without an obligation to teach, and you are required to teach to cover the other half of the stipend. However we cap the teaching you are required to do: if you teach one section of calculus, or the equivalent, and this does not pay half the annual departmental stipend we will supplement your pay up to that level. In your fifth (and subsequent) years you are required to teach to cover your whole stipend. However again we cap the teaching required: if your teach 2 sections of calculus, or the equivalent, and this does not pay the annual departmental stipend we will supplement your pay up to that level.

`Equivalence' is based on what we perceive to be the time commitment of a teaching job. We consider the following to be `equivalent' to one section of calculus:

Teaching one tutorial
CAing 2 sections of the core
CAing 2 sections of applied math
2 jobs at the Math Question Center
GCAing two courses in our department

We consider the following to be `equivalent' to two sections of calculus:

Teaching two tutorials
CAing 3 sections of the core
CAing 3 sections of applied math
GCAing 4 courses in our department
Teaching one section of calculus and CAing one section of core/applied math
Teaching one section of calculus and GCAing two courses in our dept

There are of course other possibilities, which will be judged on an ad hoc basis, but this list gives an idea of what is expected.

Every student, whether or not they have outside support, are required to have two semesters of classroom teaching experience during their time here, as preparation for their likely future role as teachers. If you are not required to teach as part of your financial aid package, then the pay for this teaching will simply supplement your other sources of support.

The department will help you to find the teaching jobs you are required to have. While we would like to accommodate your preferences for what sort of job you would like to have, we are working under many constraints. It is necessary to balance your preferences with those of other graduate students and the needs of the department. If you have done a good and conscientious job on your previous teaching assignments, you are more likely to get your preference in subsequent years. You should make your teaching plans well in advance and in consultation with the department. You should not change them at short notice.

If you are making satisfactory academic progress and if you can find the jobs, you may teach beyond the minimal requirement outlined above. If you do so, whatever money you make will be in addition to your usual stipend. In assigning teaching positions, first preference will be given to those required to teach. After that positions will be allocated to those with the strongest teaching credentials.

Here are some typical examples of the above policy. I will use 03/04 figures.

Student A in year 1 receives the full departmental stipend: $20,000.

Student B in year 2 teaches one section of calculus and receives:

half stipend - $10,000
payment for teaching - $6,315
extra subsidy - $3,685
TOTAL - $20,000

Student C in year 3 CAs two sections of the core and receives:

half stipend -$10,000
payment for teaching -$10,525
TOTAL -$20,525

Student D in year 3 GCAs two math courses and receives:

half stipend -$10,000
payment for teaching -$5,262
extra subsidy -$4,738
TOTAL -$20,000

Student E in year 4 without outside support decides not to teach and receives a half stipend of $10,000.

Student F in year 5 teaches one section of calculus and CAs one section of applied math and receives:

payment for teaching calculus -$6,315
payment for CAing applied math -$5,262
extra subsidy -$8,423
TOTAL -$20,000

Professional Development

This part of the page was put together by Stephanie Yang.

Writing papers and submitting them

Kleiman's notes on mathematical writing

Applying for jobs

Writing a CV

Example 1 and template (courtesy of Nathan Dunfield)
Example 2 and template with style file (courtesy of William Stein)
Example 3 and template

Writing a Cover Sheet

The AMS guide to cover sheets, including templates in all formats

Research Statements

Writing letters of recommendation

Senior Faculty Research Interests

Elkies, Noam	Number theory, computation, classical algebraic geometry, music
Gaitsgory, Dennis	Geometric aspects of representation theory
Gross, Benedict H.	Algebraic number theory, Diophantine geometry modular forms
Harris, Joseph D.	Algebraic geometry.
Hopkins, Michael J.	Algebraic Topology.
Jaffe, Arthur M.	Noncommutative geometry, cyclic cohomology, analysis in infinite dimensions, and constructive field theory
Kronheimer, Peter B.	Geometry and Topology.
Mazur, Barry C.	Number theory, automorphic forms and related issues in algebraic geometry
McMullen, Curtis	Riemann surfaces, complex dynamics, hyperbolic geometry
Nowak, Martin	Mathematical biology, evolutionary dynamics, invectious diseases, cancer genetics, game theory, language
Sacks, Gerald E.	Mathematical logic, logic in computer science, recursive functions and computability, E-recursion, alpha-recursion, prolog, programming, set theory and constructibility
Schmid, Wilfried	Lie groups, representation theory, complex differential geometry
Siu, Yum Tong	Several complex variables.
Sternberg, Shlomo Z.	Differential geometry, differential equations, Lie groups and algebras, mathematical physics.
Taubes, Clifford	Nonlinear partial differential equations and applications to topology, geometry, and mathematical physics.
Taylor, Richard	Algebraic number theory, modular forms, Galois representations.
Yau, Horng-Tzer	Probability theory, quantum dynamics, differential equations and nonequilibrium physics
Yau, Shing-Tung	Differential geometry, partial differential equations, topology, mathematical physics.

Junior and visiting faculty interests comprise a diverse and important addition to the department. As these appointments vary in length from one term, on the part of visitors, to three-year appointments as a Benjamin Pierce Lecturer on Mathematics, Assistant Professor of Mathematics, they will be listed annually in the courses of instruction.

How to obtain copies of past Ph.D. theses

In general, past Ph.D. theses from any university can be obtained from:

Past Harvard Ph.D. theses may be obtained directly from:

University Microfilms International
300 North Zeeb Road
Ann Arbor, Michigan 48106

Photographic Services
Widener 90
Widener Library
Harvard University
Cambridge, MA 02138
(617) 295-2129

The request must be sent in writing. They may reply with e-mail if you include your address, and will state the cost. Upon receipt of the requested dollar amount, they will send you a copy.
Since 2001, the titles of dissertations are listed online:

2001: 2001 Source:

Klenke, Tomas Antonius   Modular Varieties and Visibility   2001 June   14376
Mann, William Russell   Local Level-Raising for GLn   2001 June   14376
Pollack, Robert Jordan   On the p -adic L -function of a Modular Form at Supersingular Prime   2001 June   14376
Savitt, David Lawrence   Modularity of Some Potentially Barsotti-Tate Galois Representations   2001 June   14376
Vologodsky, Vadim   Hodge Structure on the Fundamental Group and Its Application to p-adic Integration   2001 June   14376
Warrington, Gregory Saunders   Kazhdan-Lusztig Polynomials, Pattern Avoidance and Singular Loci of Schubert Varieties   2001 June   14376
Williams, Samuel Rufus   Mod p L -functions and Analytic Kolyvagin Systems    2001 June   14376

2002: 2002 Source

Arinkin, Dmitro Olexandrovich    Fourier Transform for Quantized Completely Integrable Systems   2002 June   14593
DeMarco, Laura Grace   Holomorphic Families of Rational Maps: Dynamics, Geometry, and Potential Theory   2002 June   14593
Grushevsky, Samuel   Effective Schottky Problem   2002 June   14593
LiBine, Matvei   A Localization Argument for Characters of Reductive Lie Groups   2002 June   14593
Liu, Chiu-Chu Melissa   Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions   2002 June   14593
Mantovan, Elena   On Certain Unitary Group Shimura Varieties   2002 June   14593
Scott, Ralph H. III   Closed Self-Dual Two-Forms on Four-Dimensional Handlebodies   2002 November   14716
Trifkovic, Mak   On Mu-Invariants of Elliptic Curves over Q   2002 June   14593
Yang, Huan   Hecke Algebra Action on Siegel Modular Forms    2002 June    14593

2003: 2003 Source

Chen, Jiun-Cheng    Flops and Equivalences of Derived Categories for Threefolds with only Terminal Gorenstein Singularities   2003 June   14883
Cheng, Hsiao-Bing   Li-Yau-Hamilton Estimate For the Ricci Flow   2003 June   14883
Clark, Pete L.   Rational Points on Atkin-Lehner Quotients of Shimura Curves   2003 June   14883
Jao, David Yen   Supersingular Primes for Rational Points on Modular Curves   2003 June   14883
Karigiannis, Spiros   Deformations of G2 and Spin(7) Structures on Manifolds   2003 June   14883
Liu, Yu-Ru   Generalizations of the Turán and the Erds-Kac Theorems   2003 June   14883
Lucianovic, Mark William   Quaternion Rings, Ternary Quadratic Forms, and Fourier Coefficients of Modular Forms on PGSp(6)   2003 June   14883
Pop-Eleches, Cristian   Central Values of Rankin L-series Over Real Quadratic Fields   2003 June   14883
Rasmussen, Jacob Andrew   Floer Homology and Knot Complements   2003 June   14883
Weissman, Martin Hillel    The Fourier-Jacobi Map and Small Representations   2003 June   14883

2004: 2004 Source

Coskun, Izzet    Degenerations of Scrolls and Del Pezzo Surfaces and Applications to Enumerative Geometry    2004 June    15099
Dumas, David A.   Complex Projective Structures, Grafting, and Teichmüller Theory   2004 June   15099
Lee, Edward Dole   A Modular Non-Rigid Calabi-Yau Threefold.   2004 November   16069
Manolescu, Ciprian   A Spectrum Valued TQFT from the Seiberg-Witten Equations   2004 June   15099
Marian, Alina   Intersection Theory on the Moduli Space of Stable Bundles via Morphism Spaces   2004 June   15099
Mirzakhani, Maryam   Simple Geodesics on Hyperbolic Surfaces and the Volume of the Moduli Space of Curves   2004 June   15099
Plamenevskaia, Olga   Contact Structures and Floer Homology   2004 June   15099
Ramsey, Nicholas Adam   Geometric and p-adic Modular Forms of Half-Integral Weight   2004 June   15099
Rauch, Daniel   Perturbations of the D-Bar Operator.   2004 March   15005
Rogers, Nicholas Franklin   Elliptic Curves x3 + y3 = k with High Rank   2004 June   15099
Yang, Stephanie Tze-Ping   Special Linear Series in P2   2004 June   15099

2005: 2005 Source

Green, Peter Eric  Geometricity of Local p-Adic Representations.  	2005 June  	17164
Grigorov, Grigor Tsankov  Kato's Euler System and the Main Conjecture. 	2005 June 	17164
Kaplan, Jonathan Robert  Morphlets: A Multiscale Representation for Diffeomorphisms. 	2005 June 	17164
Khosla, Deepee 	Moduli Spaces of Curves with Linear Series and the Slope Conjecture. 	2005 June 	17164
Mast, Jerrel Harlan  Pseudoholomorphic Punctured Spheres in the Symplectization of a Quotient. 	2005 June 	17164
Mohta, Vivek  Applications of Chiral Perturbation Theory. 	2005 June 	17164
Neel, Robert Weston  The Heat Kernel at the Cut Locus. 	2005 June 	17164

Birkhoff Library

The library is non-circulating. Please do not take books out of the library, even to your office Books can be removed briefly for photocopying. The Cabot library, on the first floor of the Science Center, has a much larger collection of mathematics books and journals that can be checked out.
Books can be located online and in the library card catalogue. There is a new section with calculus and books on math education (near the computer).
There is an iMac in the library for consultation of the online catalogue and related databases (e.g. Math Reviews). Please use other public computers for non-library purposes (like email, etc.)
Journals are shelved alphabetically by title. There is an alphabetized list of journals and a guide to their locations next to the card catalogue.
Please see the librarian Nancy Miller (nancy@math), for questions about the library. Her office is inside the library. Please report any missing books to her (eg by email to nancy@math).
She also welcomes suggestions for new acquisitions, either for Birkhoff or for Cabot.
Please keep the library environment quiet at all hours. If you want to have a conversation, please step out of the library. Do not use laptops or cell-phones in the library at any time.

Photos and Media