Diary Summer 2008

As usual with twitter type diaries, this is a very boring document. The reason I throw this online is that I can google it ... The summer can be summarized with quite exciting research and summer school, as well as a lot of training for the triathlon in Switzerland. I had trained 4 hours a day 21 years ago. Now it was again 3-4 hours per day. But the training had worked and things went well.
26-5-2008: Start this "twitter" diary for Summer 2008. Warning: almost everything is boring. It will be nice to see however later for me what was done on each day.
27-5-2008: Shop for a refridgerator in the morning. Problem of showing boundedness of det(diag((exp(i k alpha) - 1))/log(n) in case of rational alpha. Rhetorik page Blocher update, Blick evening page. Start course grades. Prepair summer school and add some problems to the homework. Running: pepper bridge route.
28-5-2008: Update Blocher. Numerical experiments Green function in off diagonal case. In the afternoon preceptor meeting. Work on estimation of determinant. Grades finalize. Reading in proof of Bourgain of determinant estimate. Do we have in the Jacobi case still the same polynomial growth? Running: MIT route, swimming for 30 minutes. 5-29-08
30-5-2008: Friday Biking in over Walham-Newton-Brookline to work and back detour 40 km. Archive, send letters to students. Work on determinant. Run the fresh pond.
31-5-2008: Saturday morning work on rhetorics. Buy soil for tomatos and bring it with the bike home. Almost breaks the handlebar. 5 times 4.5 km round trips in Arlington training. Watch "Fish called Wanda" again.
1-6-2008: Sunday morning 62 km ride to Wilmington, Bedford, Concord, Lincoln. Afternoon: bike with family to Lexington. Experimental: the width of the fluctuations of det(L(n,c,alpha)) becomes smaller for larger c in Toeplitz case. How do we factor out the exponential growth? A brute force estimate of the determinant is not going to work. Onion and Jerk movie. Pay Bills.
2-6-2008: A 62 ride to Lexington Center, Waltham, Newton, Watertown, Cambridge. Back along Medford, Malden, Melrose, Ell Pond,Fells, Winchester,Lexington. Work on determinant: estimating the minors det(A(n,m)/kappa) < N exp(-c|n-m|) seems no problem for suitable kappa. The problem to estimate det(A)>1/N^2 is a bigger problem. Do we get through with det(A(gamma')) < n^{sqrt(n)} for |gamma|=s and gamma' is the complement?
3-6-2008: Use the nice sunny weather to ride in the morning over Waltham, Newton and back around the Fels and Walthan over Lexington. Letter for Albert in the morning. I definitely need a new wheel on the bike. Movies: ghostbuster and caddyshack.
04-6-2008: Help Tom to move. He drives today to Texas. Think the rest of the day about the QR decomposition in the KAM situation. Can we estimate it? We always can do a QR decomposition but the inverse might not always exist. Check this.
05-6-2008: L=QR experiments. L^T L = R^T R and its invers R^-1 R^-1^T. Can we estimate the growth of the norms of the columns of R^-1?
06-6-2008: Swim 2 km (cramp), short run in rain. Work on TW function computation. Computation of G_nm =u_n v_m works well. There are now three ways, we are stuck. Cramer: we need to show that det(L^n)/l^n stays polynomially bounded. Titchmarsh: the cohomology functions u^+,u^- stay polynomially bounded. Gram-Schmidt: The l^2 norms of the columns of R^-1 stay bounded. Literature search: 15-10 years ago, in the libraries, I still could check thousands of articles. Now, with online search, one has to look at 10'th of thousands of articles about a topic.
07-6-2008: Morning: thought that reduction to triangular matrix would work. This would explain the polynomial boundedness. We need an abstract theorem about S_n = sum_{k=1}^n f(x+k \alpha) for a nonanalytic f. How fast does this sum grow if E[F]=0? When does it grow polynomially? Bike tour with Ben around Fels, Woburn in hot weather. Sprints in the evening on the 4.5 km round tour. Rhetorik work.
08-6-2008: 2 and a half hour bike tour around Fels to Andover Lowell, 82 km. Does Localization give a way to invert L? It seems that 0 is nonresonant. If it is possible to label the eigenvalues? Explanation for the almost periodic random walk in terms of the variation. Does log(m^+) have bounded variation?
09-6-2008: Bike in to Harvard over Bentley college. latex2html routine with image problems. the function log(m^+) has not bounded variation but we can jump over times when m^+ is close to 0 or infinity because it happens in the pattern bounded -> small -> large -> bounded.
10-6-2008: On Denjoy-Koksma: whether log(m^+) has bounded variation is not clear. Variation increases for finer partitions but less and less. Make 120 km bike ride through Dunstable, Tyngsboro, Lowell, back along 4.
11-6-2008: Drive over Bentley to Harvard 20km. Nice day for run over Science museum. Work on KAM document, especially programming. Movie: Beawolf. Do we always have hyperbolicity for periodic approximations?
12-6-2008: Work on KAM document. Especially spectral pictures. Ride over Lincoln, Wayland, Sudbury, Maynard, Acton, Carleisle. For which c and alpha=p/q is A^(q-1)(x) uniformly hyperbolic for all x? We have more chance with q-1 than with q.
13-6-2008: A latex2html implementation with HTML inclusion is handy in general. Understand the structure of where the Lyapunov exponent is the average in the x-c plane.
14-6-2008: Saturday. Work on rhetorics. Bike with Ben to Concord. Work on p/q problem, where is the boundary. Seems difficult. Scaling argument?
15-6-2008: Bike through Walden Pond, Acton, no rain fortunately. Family time. Read Jitomirskajas paper. Prepair for Monday. We watch "Flawless" again.
16-6-2008: Meet with John in the morning. Change office machine from space to matter. Read a bit in Jitomirskajas paper. Try out sproutcore.
17-6-2008: Work in Lexington's Starbucks in the morning and read J. paper as well as a bunch of preprints. Noon bike ride to Bedford, Billerica, Willmington, Reading, (65km) got lost in North Woburn in some dead ends.. Jumper movie. Reorganization of files, summerschool prep as well as some rhetorics in the evening.
18-6-2008: In Jerry King: the art of mathematics: there are two trees which have the same number of leaves. Drive over Belmont to Harvard, meet with Chris, work on Denjoix, swim 3.5 km (cramp comes now only after an hour), run to Boston university and bike back over Weston with bike accident (50 km in total, difficult to find way back over Cambridge reservoir). My back wheel is now completely toast. Watch "Chaos theory" in the night and finish Denjoy.
19-6-2008: Swam at noon, but felt the arms, run up the river. Brought bike wheel to shop but it can not be fixed well. Bike back with wheel on backpack.
20-6-2008: Work with John, letter for Albert. The new Sun Fire server works fine with Raid 5, Mathematica tests show that it is a tiny bit faster than my new office machine, as the CPU clock speed would expect. Small run around Fresh pond. Work on rhetorics in the evening.
21-6-2008: On the longest day of the year, a 100km bike ride to Medford, Malden, Melrose, Wakefield, North Saugus, Lynnfield, Middleton, Lawrence, Andover, Lowell, Tewksbury, Willmington, Woburn, Winchester, Medford, Arlington. Walk with Ben to the Turkey hill. Starbucks: how to overcome the problem that L might have an eigenvector. We need to modify implicit function theorem. Some work on rhetorics.
22-6-2008: Morning sprints onto Robbins farm. Bike ride with Ruth and Ben to Walden pond. Rhetorik updates. Work on density assumption in implicit function theorem and some preparation for the summer school.
23-6-2008: Work with John on implicit function theorem. Exchange student list with Robert Winters. Get ready for summer school. Upgrade Gutsy-Hardy at home fails with gtk library problems, needs complete reinstall. Rule: never do a distro upgrade but reinstall.
24-6-2008: First class summer school and meet with students in the afternoon. Bike back in a hail storm. Never have seen something so extreme. I bike with the pedals in the water. Work in the evening some more on the implicit function theorem. If f is twice differentiable and f'(y) h = - f(x) has a solution h for a dense set of y near x, then there is a z with f(z)=0.
25-6-2008: John can prove the theorem. Second lecture today. Swam 1 km and ran the MIT route. Still some heel problems. Evening: switch defect mac with old Dell linux. I think there is an argument that a dense set of KAM operators has no 0 eigenvalue. If Lv=0 in an open set V, then L'v is perpendicular to ker(L) because Lw=0 implies (L'v,w) = 0. But this is (-Lv',w). Now perturb with respect to the k'th side diagonal: (L'v,v) = sum v_n_k v_n + v_n-k v_n implying (S^kv,v) =0, where S is the shift. But after a Fourier transform this means all integrals exp(i n x) f^2(x) = 0. By Fourier, f=0 and so v=0. This argument assumes that v changes smoothly, but v' = L^-1 (L'v) is defined if we are localized. Trouble if we have an eigenvalue but no localization.
26-6-2008: The old refrigerator is finally out. Lecture on cross product with motor demonstration etc. Magnets are so strong, they produce sparks, when snapping them back. Half of the lecture as usual. When going faster, the Run to Freshpond a bit painfull. Have headache. Functional analytic stuff. Density proof attempt.
27-6-2008: Work with John, his proof works well. The density result needs some assumption. Dan Paradies comes with Sobolev questions. At the Mac, the swimming lanes are full. I run the Science Museum tour and get soaked from a thunderstorm on the way back. Pick up a parking tool for my wheels, and later the racing material at Marathon sports. The Rheinolds wheels work well, I gave it a spin on the Arlington hill. Work on rhetorics. Work on Ulam server setup.
28-6-2008: Work on rhetorics. 50 km Ride to Saugus with new wheels, through Breakheart reservation around Lake Quannapowitt. Walk with Ben through Arlington, near Turkey hill and dinner in Panera. Evening: eat the first anglecot, a new apricot fruit with white skin which is a mixture of a Moroccan and Iranian apricot. Spagetti for dinner as preparation for race tomorrow. See movie "Blackops"
29-6-2008: Charles river race run. I felt less in shape, but I was 20 seconds faster than last year. Short bike ride to Lexington with Ruth and Ben. Just avoid thunderstorm but still eat outside afterwards. Prepair a bit on Siegel, where we need to update an upper triangular matrix.
30-6-2008: Get up early. After some maintainance work, I order tubes for bike, then bike in over Newton 30 km. Bike works well. Work with John on Siegel theorem in the morning. Swim 1km and run MIT route, office hours in the afternoon, bike back over Fells, Winchester. Payments in the night.
01-7-2008: Teaching in the morning. Run the MIT route in the noon. Don't get much done in the afternoon besides preparing for the next day. Work on some stuff for Ruth in the evening.
02-7-2008: Drive in through Lexington, Belmont, Nice morning, but weather closes. Talk with Shlomo about his new course. Lazy run in the noon and work a bit on a linear algebra problem. Meet John Boller who teaches game theory in summer school.
03-7-2008: Teaching in the morning. Run in the sun to Bunker hill monument. Still feel the legs from the race. Eat the first time in the "Market" at Harvard square. In the afternoon some work on Siegel also illustration and in the evening some work on rhetorics.
04-7-2008: 3 hour, 90 Km bike ride in the rain to Stoneham, Wakefield, Saugues, Lynn, Swampscott, Nahant. A bit erratic because I had expected an other route. Rhetorik work.
05-7-2008: Fast bikeride 35 km/h average over Lexington, Woburn, Winchester. Rhetorik work. Start exam. Rebuild harddrive at homecomputer with fresh Ubuntu install. Everything works smooth. Think a bit about Denjoy-Koksma in special case of Siegel.
06-7-2008: 31.3 km/h average ride to Groton, over 100 km. I feel getting stronger. Afternoon bike ride with Ruth and Ben to Lexington and shop in Trader Joe. After eating outside, write first midterm exam and watch "Terminal".
07-7-2007: Ride in over Bentley college and come a bit late to meeting with John. Use the sunny weather to run the Bunker hill route along freedom trail. After office hours "milk" drive through Stoneham along 23 freeway.
08-7-2008: Nice sunny day. Come in early for a student and therefore ride in directly over Belmont. Lecture on Curves in the morning. Run the MIT route from Hemenway. Bike back through newly found street through Medford, Winchester, Woburn over the hill but turn left near the TV antenna station, which has more elevation.
09-7-2008: Training: swim 1K, run Science center route, bike in directly and only short detour in the evening, because of thunderstorm. Set-up problems in Siegel. Office hours in the afternoon. Watch movie "dimensions" Jos Leys Etienne Ghys and Aurelien Alvarez which shows the power of Povray for teaching purposes. Pedram has mentioned to me this beautifully done project.
10-7-2008: Midterm exam. Even so it had been raining, this was a hot night. Get up early. Record "math" scene from Fahrenheit 451. Family dinner at panera bread and ice cream.
11-7-2008: Bike in to work directly. Late out of sequence exam and work with John. Things are tougher than we thought to setup things. Swim 1 K in very busy pool and run science center route. Dan drops by. Finish up exam solutions and pick up Ana Taquera burritos before going home. Shop in Food master and work outside at the table. I'm eager to try out the new firmware for the ipod touch but it does not work yet. The apple store is flooded.
12-7-2008: Bike Ride to Nashua in New Hampshire along 4. Felt well on way in, but it was harder back with head wind and less sunny weather. Maybe it was a Snickers bar, but I got headache later on. It was 85 km ride. Work also on rhetorics and do some math in Starbucks in the late afternoon. Tried several times to upgrade the firmware on my ipod touch. Each time the iPod is rendered bricky and has to be reset in an other account.
13-7-2008: Beautiful sunny 40 K ride through Lincoln, Waldenpond (along 117-126 routes), Concord, passing Hancom air field. In the afternoon, 25 K bike ride with family to MIT, where Ben will start his camp tomorrow. We eat on Campus some burritos and take the way along the river on the Boston side. Got a flat tire. Work in the Arlington Center Starbucks for an hour in the evening. Give the Ipod touch upgrade an other try but it still wont work. We eat outside in the night.
14-7-2008: Looks like it's going to be a sunny week. Ride in over Waltham-Bentley. After meeting with John, and a student see Robert in the noon. Make a Fresh pond run. It got a bit cooler. I drink a latte in the new physics coffee shop. After office hours, the bike back trip over Stonham with a "tank stop" at the crossing near 93. I drive a bit more directly to Waltham and come back along Ridge to Lexington.
15-7-2008: Ride in directly again through Belmont. Instead of going to the faculty reception, I make a longer ride along 117 to Maynard Acton. In West Concord again flat tire. Loose my bike computer. Ride fast back on 2. Eat with Ben a BLT sandwich from AA outside. Ben had his first day at the modding camp. Problems with analyticity in Siegel. I'm no more sure whether the Green function decays fast enough.
16-7-2008: Ride in directly through Lexington-Belmont to come earlier to class. Pick first up the sticker from Arlington works. It's a hot day and I had a nice run through Broadway-MIT from Hamingway with a salad at the physics bar, where I see also some old physics students. Bike back over Waltham and "Ruth hill". Dinner with Ben in Steerhouse. Remove finally the old fridge and washer. Its hardly on the street, when some private van picks it up. Start working on second midterm exam.
17-7-2008: Get up early at 4 since I have to be early to work with problem sessions. Have also problem sessions in the afternoon. Dan comes to ask about some functional analysis stuff.
18-7-2008: An easy Friday. Do not plan to work out hard with the bike. Ran the MIT route from Hemenway. Felt good running. A psychology student asks about building new addition and multiplication structures. I show him some strange things like 1-2+4-8+... = 1/3 (geometric series regularization) or 1+2+3+4+5+... = 1/12 (zeta function regularization). Buy Burritos as usual on Friday. The new bike things arrive. New saddle, shorts and helmet. Give it a spin in the evening on the Freeway.
19-7-2008: After some rhetorik work (the Schmid-Nef story is a ridiculous Selvila episode but became a media frency), make a long ride through Ipswich-Gloucester. The new saddle and shorts make the ride pleasant. Took me 4 1/2 hours and come back along the beach with headwind. The bike works well and I feel stronger. Start to work on the talk for the talk on Wednesday. Work shortly in Starbucks in the evening. The decay problem in Siegel bothers me a lot. Try some conjugation tests.
20-7-2008: It is less sunny and humid this Saturday and there are thunderstorms in the afternoon. I had been lucky yesterday. I only ride the bike for an hour around the Waltham tower hill. We eat outside in the evening. The neighbors cat comes to visit frequently. Just one year ago, the Harry potter many took place. I work a bit more on the talk and make photos. Decay problem is not solved. Try weighted Banach spaces. Finish the draft of the second midterm and the Mathematica lab.
21-7-2008: The Siegel approach seems dead. Interesting problem of John: sum /n. Does it converge? For Siegel, I tried several things like changing the Banach space, the norm, changing the functional. Need to prepair for the Wednesday talk. Setup Mathjobs a bit late this year.
22-7-2008: Rhetorik work early in the morning. Teaching in the morning, Do several things and finalize the exam. Run in the noon the MIT run. I'm lucky with the weather. Bring the exam in the evening to the printer and buy in Gardulo some nice things. Bring Buritos and eat outside with Ben. Work the rest of the evening at the presentation.
23-7-2008: Lecture in the morning. Rainy day. I drive in with my heavy bike. Continue to work on the presentation and go running only late. Before the talk, Jose comes by. He will film the talk. After the talk, we go for dinner in border cafe.
24-7-2008: Exam day. The exam goes well. 78 average. Robert drops by at noon. He knows a lot about the Middlesex Chanel and I realize that my tours to Lowell have been following the channel pretty well. After a short gym visit (weights and a shorter run) I grade in the afternoon. It is rainy and I can not grade outside on the terasse to have a chance to finish during the day. Work a bit on the Denjoy-Koksma problem and think about Johns almost periodic Dirichlet sum.
25-7-2008: Friday morning work with John. A student discusses hyperbolic geometry, then running through Bunkerhill, a bit extended along the pears. I feel ok running. In the afternoon, some light work, Dan comes and asks about a problem on Sobolev spaces which needs Poincare-Friedrichs. The usual Ana's Taqueria burito, which we eat outside, visist by three friends of ben. I do rhetorik work until 1 AM so that I can go to a bike ride tomorrow.
26-7-2008: Saturday ride to Mount Wachusetts on a sunny day. I drove partly wrong on the 140 but still it took me 7 hours to be back. I feel ready bike wise for the triathlon. Go to eat with Ben in Panera Bread and shopping with the bike, then work a bit in Starbucks. Play chess outside in the evening.
27-7-2008: A fast bike ride of an hour. We all go for a bike ride before the rain comes. Eat outside.
28-7-2008: Monday. Bike in over Belmont. In the evening, ride though Winchester, Reading along the 62 to Waltham, "milk" stop. Office hours.
29-7-2008: Tuesday. Run the Bunker hill route a bit extended along the docks. In the evening, ride over Mystic lakes
30-7-2008: Wednesday. Run through the park near the science museum which is now open and cross over the tracks to north station. Its a nice day.
31-7-2008: Thursday. Bike in with my usual bike. Meet with a student early. Go from lecture directly to the gym and swim the entire distance in the noon, then run the Science museum route. Pinnocio pizza and Burdicks, where I work a bit on the convergence of the Dirichlet series. It does not look so good but in the evening, it is better again.
01-8-2008: Friday: Am erster August in Deutsch: In einer Woche ist der Triathlon. Fahre ueber Bentley College (neue Huegelroute neben reservoir) hinein. Schoener morgen. Arbeite mit John ueber fastperiodische Dirichletreihen. Laufe locker die MIT Brücke. Nach Pizza, Gartenkaffee im Center for adult education und Soya Milch. Dan fragt ueber 4-1-8 stencil bei der Laplace disretisierung. Fahre Heim ueber die Mystic lakes und die steilere Fernsehturm route ueber Lexington. Essen Buritos draussen. Arbeite etwas an rhetorik waehrend Film "die Inlaws" laueft. Der Wetsuit ist angekommen.
02-8-2008: Get up relatively early and start working. Update diary entries of the week. Think about analytic continuation of almost periodic Dirichlet series. Commutation formula. Its exciting. Short one hour bike ride along Lowell street with variants through Burlington. Work on rhetorik and start exam.
03-8-2008: Work on exam. Paying bills. Bike ride with family almost falls into the water but we were lucky. My bike ride in the morning through Medford, around the Fells was sunny but I got into a rain shower in Lexington.
04-8-2008: Drive in directly. Work with John and summer school student. Office hours in the afternoon. Light run around fresh pond. Take it easy now. Shop some travel stuff and bike shirt. Nice light bike ride over Belmont, Waltham. Finalize the exam in the evening. Doubts that for irrational alpha, we can do analytic continuation of almost periodic Dirichlet series.
05-8-2008: Green theorem lecture. Work on rhetorik to have the weekend free. Exam submission to the printer. Tomorrow will be the travel to Switzerland. Still to check that everything is there.
06-8-2008: Bike in during rain with my bag on the back. Lecture on divergence theorem. The final exam arrives. Meet with students after class and at 3. Only a light run in the noon. At 5:15, the bicycle ride to the airport. Crazy to use the bike along the 1A in the tunnel. Especially with the heavy bag on the back. At the airport, there are problems with the bike: they only have plastic bags, no box. I wonder how well it will survive. At the airport, I can relax a bit finally and change cloths.
07-8-2008: The Flight to Zuerich. If we can do analytic continuation of sum_n sin(n alpha)/n^s, then we also can define arbitrary derivatives of this Fourier series using the difference differential relation f(s-2,alpha)=-f''(s,alpha). If the left hand side has been defined by analytic continuation, the right hand side is defined. The bike arrives well and Pipo and Regi take me from the airport directly to Ascona, where we sleep. One stop at the Gotthard restaurant. Nice coffee shops and pasta dinner at the lake. Our hotel is near all these beach shops.
08-8-2008: Triathlon day. We get up at 6, pack up and drive from Ascona to Locarno. The thunderstorms and heavy rain in the night are gone and perfect weather. It is even hot at the beach, especially in the wetsuit. The 1 hour swim goes well. Without glasses, I can still just follow the sun. A snag when changing to the bikes: the bike rack had fallen from the car and the bikes are a bit damaged. But we can start with wobbly wheels through the Leventina in the Tessin. Good weather. It even gets hot on the Tremola, which I can climb without shirt. Heavy headwind to Andermatt and despite a little bit rain, we can do the 10 hour bike trip without getting into rain. We make the same route as 21 years ago and change north of Zuerich. An accident in Zurich damages the knee of pipo and the bike and despite some good start running, From Toessegg, I get double support.
09-8-2008: I'm usually more tired and jet legged when coming without a triathlon. Nice partly sunny morning. Pipo can fix one part of the bent derailleur and I give the bike with still wobbly wheels a spin around the Cholfirst. Some Swims in the pool and read a bit outside. And nice dinner with family in the evening.
10-8-2008: After a short run in the morning to the Cholfirst and a swim in the pool, a trip home with Swiss airlines. Packaging of the bike was no problem at this time. A pleasant flight with an interesting discussion with a flight neighbor on e-voting. In the evening unpacking and cleaning up.
11-8-2008: One feels that the summer gets to an end. It is no more hot. Work in the morning on some rhetoric updates. Tomorrow is the exam.
12-8-2008: The final exam goes well. All but one student take the exam. After a noon run, I grade all day.
13-8-2008: Last day before the flight. I finish the grades, make some last buys.
14-8-2008: Manage to reserve rooms for the fall exam days in the morning. Flight to Switzerland over Frankfurt. Went well.
15-8-2008: Arrive in Zuerich. Arrive by train, where Regi takes us from the station. We eat in Uhwiesen with Pipo, Regi and kids.
16-8-2008: Evening dinner in Pipos house. Tomorrow, we will already leave for Wallis.
17-8-2008: We arrive from Visp. Neuhausen 10 o clock, Ausserberg 1:30. We arrive with a little detour. I make a run to the Raaft. We eat Fondu.
18-8-2008: A little tour to the Baltschiedertal. Afterwards, I run to Ausserberg to buy some things but the store is closed. I have experimented with nessels on the knees and feel it all night.
19-8-2008: Wonderful day. We make a walk onto the Raaft. Eat a lot of berries and cherries. I cut some wood.
20-8-2008: Breakfast in the Wallis fog. But the blue sky returns. Start the Huettlibuch entry. Walk along the water line. Idea about new invariant for dynanmical systems using Dirichlet series.
21-8-2008: Come back from Wallis with the train and arrive in Neuhausen at about 6 o clock. Unlike the way in, we had been using the upper Loetschberg way passing Goppenstein, Kandersteg.
22-8-2008: Walk with Ruth and Ben in the Kohlfirst. Go to a Chinese restaurant in the evening with Regi and her Kids. Pipo is on a business trip to China. Play "Tschau-Sepp". Strange. I had been playing this a lot as a kid but did not remember the rules any more: 7: take 2, under: chose color, 8 leave out next player, ass: cover with any color. Ben and Anna play chess.
23-8-2008: Rainy day in Uhwiesen. Ben had been sick in the night and we sleep a bit longer. Work on rhetorics. Go for a short run in the forest above Uhwiesen.

Oliver Knill, Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA. SciCenter 432 Tel: (617) 495 5549, Email: knill@math.harvard.edu Twitter, Youtube, Vimeo, Linkedin, Scholar Harvard, Academia, Google plus, Google Scholar, Ello, Webcam, Fall 2017 office hours: Mon-Fri 4-5 PM and by appointment.