Celebratio Mathematica

Joel Hass was born in Tel Aviv on 3 Janu­ary, 1966, to Ju­li­an and Al­iza Hass.

His moth­er was born and raised in Jer­u­s­alem to par­ents who had emig­rated from Hun­gary (ca. 1919) to what would be­come Is­rael, then the Brit­ish League of Na­tions Man­date for Palestine. Al­iza’s fath­er was a sur­vey­or and her class­mates in­cluded fu­ture Prime Min­is­ter Yitzhak Ra­bin.

Ju­li­an Hass was born in Waid­hofen, Aus­tria in 1919 and, shortly after, moved with his fam­ily to the town of Kla­gen­furt, where he grew up in poverty. In 1939, fol­low­ing the Nazi takeover of Aus­tria, he es­caped to Palestine. It was nearly im­possible to ob­tain visas to travel, but a loop­hole al­lowed boats on the Danube, an in­ter­na­tion­al river re­quir­ing no visas, to take Jews to the Black Sea. There they trans­ferred to ships which ran a Brit­ish block­ade to drop them off on the Is­raeli shore in the dark of night. After a brief stint on a kib­butz and work­ing in con­struc­tion, Ju­li­an joined the Brit­ish army. He fought in Africa, in­clud­ing at the battle of El Alamein, and in the in­va­sion of Italy. Ju­li­an was with the first group to reach Fer­ra­monte, an Itali­an in­tern­ment camp for Jews, where his sis­ter Ida, with whom he had com­mu­nic­ated by let­ter, had sur­vived the war.

Ju­li­an even­tu­ally ob­tained the rank of ser­geant and, at war’s end, re­turned to Is­rael to start a new ci­vil­ian life. For a brief time, he was en­rolled at Hebrew Uni­versity, and there he met Al­iza who was fin­ish­ing a de­gree in chem­istry and had spent the war driv­ing am­bu­lances in Egypt and Italy.

Ju­li­an’s time as a stu­dent was short-lived; after meet­ing an Itali­an tex­tile man­u­fac­turer, he de­cided to go in­to busi­ness, and began run­ning a thread man­u­fac­turer in Is­rael, and for a while prospered as an im­port­er of tex­tiles. When the en­ter­prise fol­ded, Ju­li­an and Al­iza emig­rated to New York. The year was 1960. Tex­tiles was a dy­ing in­dustry in the US and Ju­li­an spent the re­mainder of his ca­reer work­ing for a series of fail­ing busi­nesses.

Joel and his sis­ter, Ada (who grew up to be­come a pe­di­at­ri­cian) went to pub­lic schools in Queens, N.Y. They spent a year in Lon­don from 1967–68 and the years 1969–72 in Leicester­shire, Eng­land. Joel did well in the loc­al schools, which offered good teach­ers and labs. He did par­tic­u­larly well in math — it was easy for him — and his par­ents gave him a lot of en­cour­age­ment in the sub­ject.

When the fam­ily re­turned to New York, Joel did not en­roll for his ju­ni­or year of high school. In­stead he entered Hunter Col­lege, one of the col­leges in the City Uni­versity of New York sys­tem, and a year later trans­ferred to Columbia Uni­versity. After gradu­at­ing in 1976, he went to gradu­ate school in math at the Uni­versity of Cali­for­nia, Berke­ley.

At Berke­ley he joined an il­lus­tri­ous group of to­po­logy stu­dents: Paul Melvin, John Hughes, Charles Liv­ing­ston, Cole Giller, Bill Menasco, Tim Co­chran, Daniel Ruber­man, Dav­id Schorow, Bob Gom­pf (all Kirby stu­dents); Marc Cull­er (a stu­dent of John Stallings); Pat Gilmer and Bob Has­ner (stu­dents of Emery Thomas); Bill Gold­man (stu­dent of Moe Hirsch); and Ro­ger Sch­lafly (stu­dent of Is Sing­er).

My memor­ies of Joel dur­ing his grad stu­dent days re­volve around games. We had a mixed soc­cer team in the in­tra­mur­als, and Joel, Tim Co­chran and Danny Ruber­man were three of the stars. Joel was on a couple of mem­or­able raft­ing trips, too, and was a good back­gam­mon play­er. Math­em­at­ic­ally, he had an eye for good prob­lems, liked geo­metry as well as to­po­logy, and was an in­de­pend­ent thinker, ad­ept at find­ing his own re­search prob­lems.

After fin­ish­ing his PhD in 1981, Joel had a two-year postdoc ap­point­ment at the Uni­versity of Michigan, which was de­ferred by one year so that he could par­ti­cip­ate in a spe­cial year in to­po­logy at Hebrew Uni­versity. Then fol­lowed a year at MSRI in 1984–85, the fam­ous year when the low-di­men­sion­al to­po­logy pro­gram was for­tu­it­ously joined by the op­er­at­or al­geb­ras pro­gram with Vaughan Jones, in the wake of his work on the Jones poly­no­mi­al (which had just been gen­er­al­ized to the HOM­FLYPT two-vari­able poly­no­mi­al).

Dur­ing the spring of 1985 Joel met Abi­gail Thompson and they con­tin­ued their court­ship while Joel spent 1985–86 at Hebrew Uni­versity. To­geth­er they spent 1986–87 at Hebrew Uni­versity and were mar­ried in the sum­mer of 1987. They spent the year 1987–88 at Berke­ley, where their first daugh­ter, El­lie, was born. They even­tu­ally settled at the Uni­versity of Cali­for­nia, Dav­is, where Ben­jamin Hass (1991) and Lucy Hass (1995) roun­ded out their fam­ily.

Shortly after ar­riv­ing at Dav­is, both Joel and Abby learned to kayak, and both mastered the tech­nique of rolling a kayak up­right when it is flipped in a rap­id. This led to many very en­joy­able white­wa­ter trips on Cali­for­nia rivers, usu­ally with me and the re­doubt­able Bruce Ham­mock, an ex­cel­lent bio­lo­gist.

As an es­tab­lished mem­ber of the math de­part­ment at Dav­is, Joel spent 1990–91, 2000–2001 and 2015–16 at the In­sti­tute for Ad­vanced Study; a semester at the Uni­versity of Mel­bourne (2010), and semesters at the Tech­nion (1992) and Jer­u­s­alem (2014). He was a suc­cess­ful chair of his de­part­ment from 2010–14.

Some of Joel’s fa­vor­ite pa­pers are:

1. The pa­per [1] that emerged from joint work with Mike Freed­man and Peter Scott which ex­plored the re­la­tion­ship between 3-di­men­sion­al man­i­folds and min­im­al sur­faces. The pa­per showed that least area sur­faces in­ter­sect as little as pos­sible. Meeks and Yau had pi­on­eered the ap­plic­a­tion of min­im­al sur­faces as a tool for study­ing 3-man­i­folds, ap­ply­ing their the­ory to min­im­al disks and spheres. This pa­per stud­ied min­im­al in­com­press­ible sur­faces of high­er genus. It in­tro­duced a new no­tion of the com­plex­ity of two sur­faces in­ter­sect­ing and ex­ten­ded the tower ar­gu­ment of Papakyriako­po­l­ous to ar­bit­rary sur­faces. The pa­per has be­come a stand­ard tool in the study of 3-man­i­folds.
2. The pa­per [2] con­struc­ted a met­ric on the 3-ball \( B^3 \) with neg­at­ive curvature and con­cave bound­ary. This is not pos­sible with a hy­per­bol­ic met­ric, since a hy­per­bol­ic ball can be de­veloped in­to \( H^3 \). Bill Thur­ston had guessed that such a met­ric was not pos­sible, giv­ing a rare in­stance where his in­tu­ition did not point in the right dir­ec­tion.
3. Hass and Ro­ger Sch­lafly solved the equal-volume double bubble con­jec­ture in [4]. This pa­per was one of the earli­est res­ults proved us­ing rig­or­ous com­pu­ta­tion­al meth­ods, though this later be­came quite com­mon. It showed that a stand­ard double bubble, formed from two 2-spheres meet­ing at \( 120^o \) and sep­ar­ated by a planar disk, gives the least area sur­face en­clos­ing two re­gions of equal volume.
4. The con­struc­tion of al­gorithms to solve prob­lems in to­po­logy has played an im­port­ant role in to­po­logy since the work of Dehn, Haken and Markov. A break­through in the fur­ther step of look­ing at the com­plex­ity of a to­po­lo­gic­al al­gorithm was giv­en in [3], which ana­lyzed the com­plex­ity of al­gorithms for de­term­in­ing wheth­er a knot is trivi­al. An­swer­ing a ques­tion of Thur­ston, the pa­per [3] showed that un­knot­ting lies in the class NP. This pa­per helped pave the way for the cur­rent activ­ity ex­plor­ing a large num­ber of to­po­lo­gic­al com­plex­ity prob­lems.
5. Since al­most everything we see is a sur­face, sur­face com­par­is­on arises in nu­mer­ous ap­plic­a­tions. The pa­per [5] cov­ers this area, in which Joel has been work­ing in re­cent years. He has been ap­ply­ing the power­ful tech­niques de­veloped in low di­men­sion­al to­po­logy and geo­metry to prob­lems in shape re­cog­ni­tion, in par­tic­u­lar in bio­logy and medi­cine. Much of ra­di­ology, for ex­ample, falls in­to the class of sur­face com­par­is­on prob­lems. This pa­per de­scribes a the­ory de­veloped with Patrice Koehl that has been suc­cess­fully used to com­pare and clas­si­fy sur­faces of ob­jects such as bones, pro­teins and teeth.