Peter D. Hislop
  Professor of Mathematics
  Ralph E. and Norma L. Edwards Research Professor of Mathematics, 2010-2013
  University Research Professor
 

E-Mail:

    peter.hislop@uky.edu

Phone Numbers:
 

  Office: 
  FAX: 
+1 859 257 5637
+1 859 257 4078 
Peter D. Hislop

Mailing Address:

    Department of Mathematics
    University of Kentucky
    753 Patterson Office Tower
    Lexington, Kentucky  40506-0027

For information on graduate studies in math, please see our department web page that may be found here: UK Mathematics Graduate Program web page

UK PDE/Analysis Seminar Program for Fall 2014, Spring 2015, Fall 2015, Spring 2016, Fall 2016, Spring 2017, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, spring 2020, fall 2020, spring 2021, fall 2021, spring 2022, fall 2022

The most recent schedule for the PDE/Analysis Seminar may be found here: Schedule Fall 2014. Schedule Spring 2015. Schedule Fall 2015. Schedule Spring 2016. Schedule Fall 2016. Schedule Spring 2017. Schedule Fall 2017. Schedule Spring 2018. Schedule Fall 2018. Schedule Spring 2019. Schedule Fall 2019. Schedule Spring 2020.

Recent Research Papers:

My recent research has focussed on three areas: random Schrodinger operators, geometric analysis of real and complex hyperbolic manifolds, and resonance and eigenvalue estimates. My current doctoral students are Maryam Alghafli, Ben Brodie, and Sam Herschenfeld. Joseph Lindgren and Robert Wolf graduated in May 2017. You can also check the archives for most of my recent papers.

A more complete list of my publications may be found on MathSciNet.

Upcoming Workshops:

Great Lakes Mathematical Physics Meeting 2020, 24--25--26 June 2020, Oberlin College, Oberlin OH (near Cleveland), organized by Peter D. Hislop, Ilya Kachkovskiy, Christoph Marx, and Jeffrey Schenker. Cancelled due to COVID-19: Now scheduled for June 2021 at MSU, see the webpage ofr updates.

Ohio River Analysis Meeting 10, University of Kentucky, Lexington KY, Saturday and Sunday, 28 March - 29 March 2020. Cancelled due to COVID-19: Now scheduled for March 2021 at the University of Kentucky, see the webpage for updates.

Course Material for Fall 2020:

This course will cover the basics of Riemannian geometry following the book Riemannian geometry by do Carmo (Birkhauser, 1988). We will study differentiable manifolds, Riemannian metrics, tangent and cotangent spaces, vector fields, geodesics, connections, and curvature. We will develop enough machinery to describe the spaces of constant curvature and complete manifolds. Riemannian geometry is built on the classical theory of curves and surfaces in space. It is recommended that the students look at a book such as Differential geometry of curves and surfaces by do Carmo to see the origins of the subject. We will begin on 17 August 2020. I plan to have Zoom meetings MWF 12:00-12:50. If things evolve positively, we might shift to in-person meetings. Everyone should have a scanning app for homework submission. I plan to use Canvas to post the Zoom sessions and the lectures. Hopefully, you'll get an email from me next week from Canvas.

Course Material for Spring 2020:

Course Material for Fall 2019:

Course Material for Spring 2019:

Course Material for Fall 2018:

Course Material for Spring 2018:

    MA507 and PHY507 Mathematical Methods of Physics

Course Material for Fall 2017:

    MA506 and PHY506 Mathematical Methods of Physics

Course Material for Spring 2017:

    I am not teaching any regular classes this semesters

Course Material for Fall 2016:

    MA 681 Functional Analysis

Course Material for Spring 2016:

    MA507 and PHY507 Mathematical Methods of Physics

Course Material for Fall 2015:

    MA506 and PHY506 Mathematical Methods of Physics

This is the first semester of calculus. After a review of functions, we will study the derivative and integral. ALL SIX SECTIONS MEET FOR LECTURES: MWF 2:00-2:50 in CP 153. Final Exam Review 1 , Monday, 14 December 2015, 4:00--5:30 PM , KAS 213 FINAL EXAM, Tuesday, 15 December, 6--8 PM in BS 107 (same room as all the tests). Official policy of conflicts: ``Any student with more than two final examinations scheduled on any one date shall be entitled to have the examination for the class with the highest catalog number rescheduled.'' Email me by Monday, 7 December, if you have more than 2 exams on 15 Dec. or a conflict.

Course Material for Fall 2014:

    MA 575 Introduction to Analysis

This graduate class meets MWF 11:00-11:50 AM in CB 339.

The goal of this course is to provide everyone with a firm foundation in the theory of functions of a single real variable. Although a lot of this is familiar from the calculus, we�ll carefully and rigorously study properties of functions, like continuity and differentiability, and the Riemann integral. We�ll also look at questions of convergence of sequences of numbers and functions, including the important topic of uniform convergence of functions. These are fundamental ideas that all mathematicians should be familiar with. No class the week of November 3.

    MA 114 Honors Calculus II sections 009 and 010

This is the honors Calculus II class for fall 2014 semester. Both sections 009 and 010 meet for lectures MWF 1:00-1:50 in CB 110. Note change in room!

Course Material for Spring 2014:

    MA 641 Differential Geometry

This course will cover the basics of Riemannian geometry following the book Riemannian geometry by do Carmo (Birkhauser, 1988). We will study differentiable manifolds, Riemannian metrics, tangent and cotangent spaces, vector fields, geodesics, connections, and curvature. We will develop enough machinery to describe the spaces of constant curvature and complete manifolds. Riemannian geometry is built on the classical theory of curves and surfaces in space. It is recommended that the students look at a book such as Differential geometry of curves and surfaces by do Carmo to see the origins of the subject. NEW: Classroom change to CB 341!!

    MA 113 Calculus I sections 005, 006, 007, 008

This is the first semester of calculus. After a review of functions, we will study the derivative and integral. ALL FOUR SECTIONS MEET FOR LECTURES: MWF 12:00-12:50 in CB 114. . The Final Exam is WEDNESDAY, 7 May, at 8:30-10:30 PM in CB 106. If you have a conflict, see me or email me before 30 April 2014. The Review Session is MONDAY, 5 May, from 3:30-5:00 PM, in CB 106. If you want a copy of your final or have questions about your grades, please email me. Have a good summer!!

Course Material for Fall 2013:

    MA 681 Functional Analysis

This is a course in Banach and Hilbert space theory with an emphasis on the theory of linear operators. The class meets MWF 12-12:50 in CB 343. Special class: Monday, 7 October at 4PM

    MA 113 Calculus I sections 025, 026, 027, 028

This is the first semester of calculus. After a review of functions, we will study the derivative and integral. ALL FOUR SECTIONS MEET FOR LECTURES: MWF 2:00-2:50 in CB 110. The book store may still have some copies of the book. You can also order it on Amazon. NEW: Final exam, Wednesday, 18 December, 8:30--10:30 PM in CB 118. REVIEW SESSION: Tuesday, 17 December 2013 3:30-5 PM in CB 118. Good luck with the final!

Course Material for Spring 2013:

    MA507 and PHY507 Mathematical Methods of Physics

    MA 114 Calculus II sections 005, 006, 007, 008

This is the second semester of calculus. We will study integration methods and applications. ALL FOUR SECTIONS MEET FOR LECTURES: MWF 10:00-10:50 in CP 320. NEW: Final Review: Sunday and Monday, 28 and 29 April, from 6:30-8:30 PM, in CP 153 (Sunday) and CB 102 (Monday). Final Exam, 1 May, 6-8 PM in BS 107. Alternate Final Exam, 2 May, 1-3 PM in the Mathskellar. Good luck! Room for Final Exam: BS 107 (Biological Sciences).

Course Material for Fall 2012:

    MA506 and PHY506 Mathematical Methods of Physics

Course Material for Spring 2012:

    MA 633 001 Partial Differential Equations II

  • Midterm exam on Friday, 23 March, over the material in Chapter 5.

Course Material for Fall 2011:

    MA 533 001 Partial Differential Equations

    MA 113 Sections 029, 030, 031, and 032 Calculus 1

This is the basic course in the calculus of functions of one real variable. The emphasis of Calculus 1 is differentiation, integration and applications. MEETS: MWF 12:00-12:50 in BE 148.

Final Exam on Wednesday, 14 December, 6:00-8:00 PM in the Student Center Theater. Review session: Monday, 12 December, 6:00-8:00 PM Room 110 CB.

Exam 3 is on Tuesday, 15 November, 7:30-9:30 PM, in the Student Center Theater. REVIEW SESSION: Monday, 14 November, 7:30 PM in Room CB 106 (Note change of room from last time).

Course Material for Spring 2011:

    Possible paper topics:

    Ricci flow and the Poincare conjecture (book by Morgan and Tian), see also "Recent progress on the Poincar� conjecture and the classification of 3-manifolds," J. Morgan, BAMS, (2005). "Towards the Poincar� conjecture and the classification of 3-manifolds," J. Milnor, Notices AMS, 2003.

    MA 214 Section 002 Ordinary Differential Equations:

This is a basic course on ordinary differential equations (ODEs). There are three main components: 1) first-order ODEs and modeling (chapter 1-2), 2) second-order ODEs and applications to oscillators (chapter 3), and 3) the Laplace transform and applications to initial value problems.

The final grades are posted. Good luck with everything and have a good summer! you can get copies of your final and the solutions are posted below.

  • Homework Problems

    • This course has a computer lab component using a free software package called IODE developed at the University of Illinois by P. Brinkmann, R. Jerrard, and R. Laugesen. There will be four projects during the semester. No prior knowledge of MatLab is needed. IODE also runs on GNU Octave, a free software available at: http://www.gnu.org/software/octave/. I have not used it but there are comments about using Octave on the Illinois Iode web page.

    You may now download IODE from the main IODE web page. The program works on 2007, 2008, 2009 and 2010 versions of Matlab. These are on the machines in Engineering and the library. The Save feature now works but it might still be more convenient to save your work as described next: ON SAVING GRAPHS: It is easiest to save your graphs as a Word document. This is convenient because you can put two graphs on one page and add comments! Enlarge the graph using the button on the upper right so it fills the screen. Press the "Print Screen" key on the keyboard. This copies the screen into a temp directory. Open Word and simply past the document into word. You can also type in your explanations, etc. you should then save the word document to your locker on the L-drive.

    Course Material for Fall 2010:

      MA 641 Differential Geometry

      This course will cover the basics of Riemannian geometry following the book Riemannian geometry by do Carmo (Birkhauser, 1988). We will study differentiable manifolds, Riemannian metrics, tangent and cotangent spaces, vector fields, geodesics, connections, and curvature. We will develop enough machinery to describe the spaces of constant curvature and complete manifolds. Riemannian geometry is built on the classical theory of curves and surfaces in space. It is recommended that the students look at a book such as Differential geometry of curves and surfaces by do Carmo to see the origins of the subject.

    Course Material for Spring 2010:

      MA 776 Pseudodifferential Operators and Applications:

      This course will be a self-contained course on pseudodifferential operators (PsDOs). The goal is to prove a theorem of Hormander on the asymptotic behavior of the eigenvalue counting function for an elliptic, lower-semibounded, self-adjoint PsDO on a compact Riemannian manifold. This will require us to study: oscillatory integrals, stationary phase, symbol calculus, basic properties of PsDOs (products, paramatrices), and basic Fourier integral operators.

      MA 214 Section 003 Ordinary Differential Equations:

    This is a basic course on ordinary differential equations (ODEs). There are three main components: 1) first-order ODEs and modeling (chapter 1-2), 2) second-order ODEs and applications to oscillators (chapter 3), and 3) the Laplace transform and applications to initial value problems.

    NEW: Grades are posted. You may get a copy of your final by stopping by my office. The solutions are posted below. Have a good summer!

    This course has a computer lab component using a free software package called IODE developed at the University of Illinois by P. Brinkmann, R. Jerrard, and R. Laugesen. There will be four projects during the semester. No prior knowledge of MatLab is needed. IODE also runs on GNU Octave, a free software available at: http://www.gnu.org/software/octave/. I have not used it but there are comments about using Octave on the Illinois Iode web page.

    You may now download IODE from the main IODE web page. The program works on 2007, 2008 and 2009 versions of Matlab. The Save feature now works but it might still be more convenient to save your work as described next: UPDATE on SAVING GRAPHS: If the usual save button does not work, you can save to a Word document. This is convenient because you can put two graphs on one page and add comments! Enlarge the graph using the button on the upper right so it fills the screen. Press the "Print Screen" key on the keyboard. This copies the screen into a temp directory. Open Word and simply past the document into word. You can also type in your explanations, etc.

  • Course Syllabus for MA214 003, Spring 2010

  • Instructions on how to start-up IODE using Matlab, Spring 2010

  • A Brief Guide to Matlab Syntax

  • Open Lab Hours in CB313, Spring 2010. I will hold my office hour in CB 313 on Wednesdays 4-5 PM. We can discuss the labs and homework.

  • Lab 1: Introduction to IODE and the first project, Spring 2010

  • Project 1: Due in class, Friday, 5 February 2010. You can use MatLab in the RG Anderson building computer labs, in the Science and Engineering Library lab (King South), and in CB 313 during open lab hours (schedule to be posted.) You cannot print in CB 313 so save your graphs in your locker using word, for example, and print them in another lab.

  • Comments on Project 1 compiled from reading the project reports. Please read through these comments and think about them as you do Project 2. GRADING: The lab was worth 15 points: the first ODE 3 points, and the remaining 3 ODEs were worth 4 points.

  • Project 2: Due in class, Wednesday, 3 March 2010.

  • Comments on Project 2 compiled from reading the project reports. Please read through these comments and think about them as you do Projects 3 and 4. GRADING: The lab was worth 15 points.

  • Project 3: Due in class, Monday, 29 March 2010.

  • Project 4: Due in class, Friday, 23 April 2010.

  • Notes on Exponentials, Logs, and Complex Numbers

  • Homework Problems
  • Quiz 1 Solutions
  • Quiz 2 Solutions
  • Practice Test #1
  • Test #1 solutions. (Correction: In Problem 5, the value of y_2 is 2.)
  • Quiz 3 Solutions
  • Quiz 4 Solutions
  • Practice Test #2
  • Test #2 solutions.
  • Table of formulas for Laplace transforms. This table will always be available to you during quizzes and the final exam.
  • Quiz 5 Solutions
  • Quiz 6 Solutions
  • Practice Final Exam.
  • Solutions to the Final Exam Spring 2010.

    • Course Material for Fall 2009:

      MA 677 Real Analysis II:

      This course is a continuation of Reals I taught in the spring of 2009. We will continue with the book of Stein and Shakarchi. You should be reading Chapter 6 on abstract measure theory. You should also be focussing on your paper and projects. Please see me to discuss them! A draft of you paper is due in class on 18 November 2009.

  • Course Syllabus for MA677, Fall 2009

  • Problem Set 1 due 9 September 2009.
  • Problem Set 2 due 2 October 2009.
  • Problem Set 3 due 16 October 2009.
  • Problem Set 4 due 4 December 2009.

      • MA 214 Section 003 Ordinary Differential Equations:

    NO LAB OFFICE HOUR Wednesday, 9 Dec. 3-4. There will be a review session Tuesday, 15 December, at 3 PM in 316 CB. Office Hour on Monday, 14 December 11 AM-12 PM and 4-5 PM in my office, 753 POT. ALL GRADES ARE FINAL (except the final exam grade and the lab 3 grade) AT 4PM TODAY UNLESS YOU CONTACT ME.

    We have finished all the work for our course. In chapter 6, we did sections 6.1-6.5. We will begin to review for the final exam tomorrow, Wednesday. The final exam is scheduled for: Wednesday, 16 December, 10:30-12:30, in our classroom CB 203. It is worth 180 points. I will award everyone 15 points for the lab that we were not able to do. A practice exam is posted below and you may find other practice final exams posted in pervious versions of this course below (Remember: we did not do exact ODEs.)

    This course will have a lab component using a free software package called IODE developed at the University of Illinois by P. Brinkmann, R. Jerrard, and R. Laugesen. There will be four projects during the semester. No prior knowledge of MatLab is needed. IODE also runs on GNU Octave, a free software available at: http://www.gnu.org/software/octave/. I have not used it but there are comments about using Octave on the Illinois Iode web page.

    UPDATE: You may now download IODE from the main IODE web page. The program works on 2007, 2008 and 2009 versions of Matlab. The only feature that does not work is the Save feature. Save your work as described next: UPDATE on SAVING GRAPHS: If the usual save button does not work, you can save to a Word document. This is convenient because you can put two graphs on one page and add comments! Enlarge the graph using the bottom on the upper right so it fills the screen. Press the "Print Screen" key on the keyboard. This copies the screen into a temp directory. Open Word and simply past the document into word. You can also type in your explanations, etc. Third project due date Friday, 4 December, in class. Please staple your pages together! CHANGE: Open lab in CB 313 on Wed. 2 Dec. from 3:15 - 4:00 PM only! You may turn in your projects on Monday.

  • Course Syllabus for MA214, Fall 2009

  • Notes on Exponentials, Logs, and Complex Numbers

  • Open Lab Hours in CB313, Fall 2009 (Please note the change on T and R mornings!)

  • Instructions on how to start-up IODE using Matlab, Fall 2009

  • A Brief Guide to Matlab Syntax, Fall 2009

  • Lab 1: Introduction to IODE, Fall 2009

  • Project 1: NEW! due in class, Wednesday, 23 September 2009 (read above). Try to get to CB313. Save you graphs in your locker using word, for example, and print them in another lab.

  • Comments on Project 1 compiled from reading the project reports. Please read through these comments and think about them as you do Project 2. GRADING: I will add 5 points to your score on Project 1 since it should have been worth 15 points.

  • Comments on Project 2 compiled from reading the project reports. Please read through these comments and think about them as you do Project 3.

  • Project 2: Due in class, Friday, 30 October 2009.

  • Project 3: Due in class, Friday, 4 December 2009.

  • Homework Problems
  • Table of formulas for Laplace transforms.
  • Quiz 1 Solutions
  • Quiz 2 Solutions
  • Quiz 3 Solutions
  • Quiz 4 Solutions
  • Practice Test #1
  • Practice Test #1 solutions
  • Test #1 solutions (Correction: Problem 4(c): The answer is P_0, not P_0 e.)
  • Quiz 5 Solutions
  • Practice Test #2.
  • Practice Test #2 solutions
  • Test #2 solutions.
  • Quiz 6 Solutions
  • Practice Final Exam.
  • Solutions to the Final Exam Fall 2009.

    • Course Material for Spring 2009:

      MA 676 Real Analysis I:

  • The grades have been posted online and the solutions to the final are below. I will return the final exam and PS #7 to your mailboxes. Have a good summer!

  • WEEKLY PROBLEM SESSION on Wednesdays at 4PM in CB 341. We are doing chapter 6 on Laplace transforms. Read sections 6.1-6.5. No problem session on Wednesday, 29 April. We will be reviewing all week. A final exam review is scheduled for Thursday, 7 May, at 5:30PM, room CB 333.

  • Course grades will be posted today, Monday, 11 May. The solutions to the final are posted below. You may stop by anytime to look at your final. Have a good summer!

  • Course Syllabus

  • Homework Problems
  • Table of formulas for Laplace transforms.
  • Quiz 1 Solutions
  • Quiz 2 Solutions
  • Quiz 3 Solutions
  • Quiz 4 Solutions
  • Quiz 5 Solutions
  • Quiz 6 Solutions
  • Quiz 7 Solutions
  • Quiz 8 Solutions
  • Quiz 9 Solutions
  • Quiz 10 Solutions
  • Test #1 Solutions
  • Test #2 Solutions
  • Final Exam Solutions

    • Course Material for Fall 2008:

      MA 214 Section 03 Ordinary Differential Equations:

    • MA 575 Principles of Analysis:

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  • Mathematics Department
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